SECURITIES AND EXCHANGE COMMISSION WASHINGTON, D.C. 20549
                                 SCHEDULE 13G

           Information Statement Pursuant to Rules 13d-1 and 13d-2
                  Under the Securities Exchange Act of 1934
                               (Amendment No. )*

                             Lomak Petroleum Inc.
- ------------------------------------------------------------------------------
                               (Name of Issuer)


                        Lomak Petroleum $2.03 Series C
- ------------------------------------------------------------------------------
             Convertible Preferred, convertible until 12/31/2049


- ------------------------------------------------------------------------------
                        (Title of Class of Securities)

                                   541509402
                              -------------------
                                (CUSIP Number)


                                 May 31, 1998
            ------------------------------------------------------
           (Date of Event Which Requires Filing of This Statement)


Check the appropriate box to designate the rule pursuant to which this
Schedule is filed.

[ X]  Rule 13d-1(b)
[  ]  Rule 13d-1(c)
[  ]  Rule 13d-1(d)


*The remainder of this cover page shall be filled out for a reporting person's
initial filing on this form with respect to the subject class of securities,
and for any subsequent amendment containing information which would alter
disclosures provided in a prior cover page.

The information required on the remainder of this cover page shall not be
deemed to be "filed" for the purpose of Section 18 of the Securities and
Exchange Act of 1934 ("Act") or otherwise subject to the liabilities of that
section of the Act but shall be subject to all other provisions of the Act
(however, see the Notes).

                                     -1-



(1) NAME OF REPORTING PERSON
       S.S. OR I.R.S. IDENTIFICATION NO.
       OF ABOVE PERSON

       D. E. Shaw Investments, L.P.
         13-3470777

- -------------------------------------------------------------------------------
(2) CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP **
       (a) [ ]
       (b) [x]

- -------------------------------------------------------------------------------
(3) SEC USE ONLY

- -------------------------------------------------------------------------------
(4) CITIZENSHIP OR PLACE OF ORGANIZATION

         Delaware
- -------------------------------------------------------------------------------
                  (5)  SOLE VOTING POWER
                                -0-   
NUMBER OF SHARES       --------------------------------------------------------
BENEFICIALLY      (6)  SHARED VOTING POWER
OWNED BY EACH                   61,975
REPORTING              --------------------------------------------------------
PERSON WITH       (7)  SOLE DISPOSITIVE POWER
                                 -0-
                       --------------------------------------------------------
                  (8)  SHARED DISPOSITIVE POWER
                                61,975
- -------------------------------------------------------------------------------
(9) AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
                  61,975
- -------------------------------------------------------------------------------
(10) CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES ** 
                  [ ]
- -------------------------------------------------------------------------------
(11)  PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)
                  5.4%
- -------------------------------------------------------------------------------
(12)  TYPE OF REPORTING PERSON **
                  BD, PN
- -------------------------------------------------------------------------------
                    
                   ** SEE INSTRUCTIONS BEFORE FILLING OUT!



(1) NAME OF REPORTING PERSON
    S.S. OR I.R.S. IDENTIFICATION NO.
    OF ABOVE PERSON


    D. E. Shaw Securities, L.P.
       13-3497780
- -------------------------------------------------------------------------------
(2) CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP **

    (a) [ ]

    (b) [x]
- -------------------------------------------------------------------------------
(3) SEC USE ONLY

- -------------------------------------------------------------------------------
(4) CITIZENSHIP OR PLACE OF ORGANIZATION

        Delaware
- -------------------------------------------------------------------------------
                  (5)  SOLE VOTING POWER
NUMBER OF                           -0- 
SHARES                 --------------------------------------------------------
BENEFICIALLY      (6)  SHARED VOTING POWER
OWNED BY                          207,265
EACH                   --------------------------------------------------------
REPORTING         (7)  SOLE DISPOSITIVE POWER
PERSON WITH                         -0- 
                       --------------------------------------------------------
                  (8)  SHARED DISPOSITIVE POWER
                                  207,265
- -------------------------------------------------------------------------------
(9) AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
                  207,265
- -------------------------------------------------------------------------------
(10) CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES **
                  [ ]
- -------------------------------------------------------------------------------
(11) PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)
                  18.0%
- -------------------------------------------------------------------------------
(12)  TYPE OF REPORTING PERSON **
                  BD, PN
- -------------------------------------------------------------------------------
            
                    ** SEE INSTRUCTIONS BEFORE FILLING OUT!



(1) NAME OF REPORTING PERSON
    S.S. OR I.R.S. IDENTIFICATION NO.
    OF ABOVE PERSON

        David E. Shaw
- -------------------------------------------------------------------------------
CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP **

   (a)  [ ]

   (b)  [x]
- -------------------------------------------------------------------------------
(3) SEC USE ONLY

- -------------------------------------------------------------------------------
(4) CITIZENSHIP OR PLACE OF ORGANIZATION
            United States
- -------------------------------------------------------------------------------
                  (5)  SOLE VOTING POWER
NUMBER OF                        -0-      
SHARES                 --------------------------------------------------------
BENEFICIALLY      (6)  SHARED VOTING POWER
OWNED BY                       269,240
EACH                   --------------------------------------------------------
REPORTING         (7)  SOLE DISPOSITIVE POWER
PERSON WITH                       -0-  
                       --------------------------------------------------------
                  (8)  SHARED DISPOSITIVE POWER
                              269,240
- -------------------------------------------------------------------------------
(9) AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
                  269,240
- -------------------------------------------------------------------------------
(10) CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES **
                  [ ]
- -------------------------------------------------------------------------------
(11) PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)
                  23.4%
- -------------------------------------------------------------------------------
(12)  TYPE OF REPORTING PERSON **
                  IN
- -------------------------------------------------------------------------------
            
                    ** SEE INSTRUCTIONS BEFORE FILLING OUT!



ITEM 1(a). NAME OF ISSUER:

Lomak Petroleum Inc. (the "Company")

ITEM 1(b). ADDRESS OF ISSUER'S PRINCIPAL EXECUTIVE OFFICES:

500 Throckmorton Street, Fortworth, TX 76102


ITEM 2(a). NAME OF PERSON FILING:

D. E. Shaw Investments, L.P. ("InvLP")
D. E. Shaw Securities, L.P. ("SecLP")
David E. Shaw ("David Shaw")

ITEM 2(b). ADDRESS OF PRINCIPAL OFFICE OR, IF NONE, RESIDENCE:

120 West 45th Street, 39th Floor, Tower 45, New York, NY  10036

ITEM 2(c). CITIZENSHIP:

InvLP is a limited partnership organized under the laws of the State of
Delaware.

SecLP is a limited partnership organized under the laws of the state of
Delaware.

David Shaw is a citizen of the United States.

ITEM 2(d).  TITLE OF CLASS OF SECURITIES:

Lomak Petroleum $2.03 Series C

Convertible Preferred, convertible until 12/31/2049 (the shares)

ITEM 2(e). CUSIP NUMBER:

541509402

ITEM 3. IF THIS STATEMENT IS FILED PURSUANT TO RULES 13d-1(b), 13d-2(b), OR
13d-3(b), CHECK WHETHER THE PERSON FILING IS A:

(a) [x] Broker or dealer registered under Section15 of the Act

(b) [ ] Bank as defined in Section 3(a)(6) of the Act

(c) [ ] Insurance Company as defined in Section 3(a)(19) of the Act

(d) [ ] Investment Company registered under Section 8 of the Investment
        Company Act

(e) [ ] Investment Adviser registered under Section 203 of the
        Investment Advisers Act of 1940

(f) [ ] Employee Benefit Plan, Pension Fund which is subject to the
        provisions of the Employee Retirement Income Security Act of 1974 or
        Endowment Fund; see Rule 13d-1(b)(1)(ii)(F)

(g) [ ] Parent Holding Company, in accordance with Rule 13d-1(b)(ii)(G); see
        item 7

(h) [ ] A Savings Association as defined in Section 3 (b) of the federal 
        Deposit Insurance Act (12U.S.C. 1813)

(i) [ ] A church Plan that is excluded from the definition of an investment 
        company under section 3 (c)(14) of the Investment Compnay Act of 1940 
        (15 U.S.C. 80a -3); and



(j) [ ] A Group, provided that all the members are persons specified in 
        accordance with section 240.13d-1(b)(1)(ii)(A) through (I)

If this statement is filed pursuant to Rule 13d-1(c), check this box. [  ]

ITEM 4. OWNERSHIP.

(a) Amount beneficially owned:

InvLP:             61,975 Shares
SecLp:            207,265 Shares
David Shaw:       269,240 Shares

(b) Percent of class:

InvLP:            5.4%
SecLP:           18.0%
David Shaw:            23.4% (based on the 1,149,840 Shares outstanding as of 
                       March 31st,1998 as stated by the Company `s quarterly 
                       report filed May 15th ,1998.)

(c) Number of shares as to which such person has:

(i) sole power to vote or to direct the vote

InvLP:                     -0-
SecLP:                     -0-
David Shaw:                -0-

(ii) shared power to vote or to direct the vote

InvLP:            61,975
SecLP:           207,265
David Shaw:      269,240


(iii) sole power to dispose or to direct the disposition of

InvLP;             -0-
SecLP:             -0-
David Shaw:        -0-

(iv) shared power to dispose or to direct the disposition of

InvLP:            61,975
SecLP:           207,265
David Shaw:      269,240

David Shaw owns directly no Shares. By reason of Rule 13d-3 under the
Securities Exchange Act of 1934 and by virtue of David Shaw's position as
President and sole shareholder of D. E. Shaw & Co., Inc., the general partner
of D. E. Shaw & Co., L.P., itself the general partner of InvLP and SecLP,
David Shaw may be deemed to 

                                     -6-


own beneficially 269,240 Shares, comprising the 61,975 Shares owned directly
by InvLP and the 207,265 Shares owned directly by SecLP. Therefore, David Shaw
may be deemed to beneficially own approximately 23.4% of the outstanding
Shares. David Shaw disclaims beneficial ownership of such 269,240 Shares.

ITEM 5. OWNERSHIP OF FIVE PERCENT OR LESS OF A CLASS.

Not applicable.

ITEM 6. OWNERSHIP OF MORE THAN FIVE PERCENT ON BEHALF OF ANOTHER PERSON.

No person other than each respective owner and general partner referred to
herein is known to have the right to receive or the power to direct the
receipt of dividends from, or the proceeds of the sale of, the Shares.

ITEM 7. IDENTIFICATION AND CLASSIFICATION OF THE SUBSIDIARY WHICH ACQUIRED THE 
        SECURITY BEING REPORTED ON BY THE PARENT HOLDING COMPANY.

Not applicable.

ITEM 8. IDENTIFICATION AND CLASSIFICATION OF MEMBERS OF THE GROUP.

Not applicable.

ITEM 9. NOTICE OF DISSOLUTION OF GROUP.

Not applicable.

ITEM 10. CERTIFICATION. (if filing pursuant to Rule 13d-1(b))

By signing below D. E. Shaw Investments, L.P., D. E. Shaw Securities, L.P.,
and David E. Shaw certify that, to the best of their knowledge and belief, the
securities referred to above were acquired and held in the ordinary course of
business and, were not acquired and are not held for the purpose of or with
the effect of changing or influencing the control of the issuer of the
securities and were not acquired in connection with or as a participant in any
transaction having such purposes or effect.



                                  SIGNATURE

         After reasonable inquiry and to the best of their knowledge and
belief, the undersigned certify that the information set forth in this
statement is true, complete and correct. A Power of Attorney, dated January
14, 1997, granted by David Shaw in favor of Daniel Fishbane, is attached
hereto.

June 04, 1998

                                    D. E. SHAW INVESTMENTS, L.P.

                                    By: D. E. SHAW & CO., L.P., as
                                        General Partner

                                    By: /s/ Daniel Fishbane
                                        ---------------------------------------
                                            Managing Director

                                    D. E. SHAW SECURITIES, L.P.

                                    By: D. E. SHAW & CO., L.P., as
                                        General Partner

                                    By: /s/ Daniel Fishbane
                                        ---------------------------------------
                                            Managing Director

                                    DAVID E. SHAW

                                    By: /s/ Daniel Fishbane
                                        ---------------------------------------
                                            Attorney-in-Fact for David E. Shaw

                                     -8-



                               POWER OF ATTORNEY
                              FOR CERTAIN FILINGS
                     UNDER THE SECURITIES EXCHANGE ACT OF
                                     1934

I, DAVID E. SHAW, hereby make, constitute and appoint each of:

Lou Salkind,

Stu Steckler,

Anne Dinning and

Danny Fishbane,

acting individually, as my agent and attorney-in-fact, with full power of
substitution, for the purpose of, from time to time, executing in my name, my
individual capacity and/or my capacity as President of D. E. Shaw & Co., Inc.
(acting for itself or as the general partner of D. E. Shaw & Co., L.P.) all
documents, certificates, instruments, statements, other filings and amendments
to the foregoing (collectively, "documents") determined by such person to be
necessary or appropriate to comply with ownership or control-person reporting
requirements imposed by any United States or non-United States governmental or
regulatory authority, including without limitation Forms 3, 4, 5, 13D, 13F and
13G required to be filed with the Securities and Exchange Commission; and
delivering, furnishing or filing any such documents with the appropriate
governmental or regulatory authority. Any such determination shall be
conclusively evidenced by such person's execution and delivery, furnishing or
filing of the applicable document.

This power of attorney shall be valid from the date hereof.

IN WITNESS WHEREOF, I have executed this instrument as of the date set forth
below.

Date:  January 14, 1997

DAVID E. SHAW

/s/ David E. Shaw
- ----------------------------
New York, New York