UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549


                                  SCHEDULE 13G


                    Under the Securities Exchange Act of 1934

                               (Amendment No. 2 )*




                              LOMAK PETROLEUM, INC.
- --------------------------------------------------------------------------------
                                (Name of Issuer)

                                  Common Stock
- --------------------------------------------------------------------------------
                         (Title of Class of Securities)

                                    541509303
- --------------------------------------------------------------------------------
                                 (CUSIP Number)

                                December 31, 1998
- --------------------------------------------------------------------------------
             (Date of Event Which Requires Filing of this Statement)

Check    the  appropriate  box to  designate  the rule  pursuant  to which  this
Schedule 13G 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 the
disclosures provided in a prior cover page.

The information required in the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the  Securities  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).








                               CUSIP NO. 541509303
- --------------------------------------------------------------------------------

(1)   Names of Reporting Persons.  I.R.S.  Identification  Nos. of Above Persons
      (entities only):  Palisade Capital Management, L.L.C., Tax ID#: 22-3330049
- --------------------------------------------------------------------------------

(2)     Check the Appropriate Box if a Member of a Group (See Instructions)
        (a)                    (b)
- --------------------------------------------------------------------------------

(3)     SEC Use Only
- --------------------------------------------------------------------------------

(4)     Citizenship or Place of Organization:  New Jersey
- --------------------------------------------------------------------------------

Number of Shares Beneficially Owned by Each     (5) Sole Voting
      Reporting Person With                           Power:             222,141
                                                (6) Shared Voting
                                                      Power:               --
                                                (7) Sole Dispositive
                                                      Power:             222,141
                                                (8) Shared Dispositive
                                                      Power:               --
- --------------------------------------------------------------------------------
(9)   Aggregate  Amount  Beneficially  Owned by Each Reporting  Person:  222,141
      (all such  shares  the  reporting  person  has the right to  acquire  upon
      conversion of convertible securities issued by the Issuer)
- --------------------------------------------------------------------------------

(10)  Check if the Aggregate Amount in Row (9) Excludes Certain Shares (See 
Instructions)
- --------------------------------------------------------------------------------

(11)  Percent of Class Represented by Amount in Row (9): 1.0%
- --------------------------------------------------------------------------------

(12)  Type of Reporting Person (See Instructions):  IA
- --------------------------------------------------------------------------------




Item 1(a).  Name Of Issuer:  Lomak Petroleum, Inc.
- --------------------------------------------------------------------------------

Item 1(b).  Address of Issuer's Principal Executive Offices:  500 Throckmorton 
Street, Ft. Worth, Texas 76102
- --------------------------------------------------------------------------------

Item 2(a).  Name of Person Filing:  Palisade Capital Management, L.L.C.
- --------------------------------------------------------------------------------

Item 2(b).  Address of Principal  Business  Office or, if None,  Residence:  One
Bridge  Plaza, Suite 695, Fort Lee, NJ 07024
- --------------------------------------------------------------------------------

Item 2(c).  Citizenship:  New Jersey
- --------------------------------------------------------------------------------

Item 2(d).  Title of Class of Securities:  Common Stock
- --------------------------------------------------------------------------------

Item 2(e).  CUSIP No.:  541509303
- --------------------------------------------------------------------------------

Item 3. If This Statement Is Filed Pursuant to  ss.240.13d-1(b)  or 240.13d-2(b)
or (c), check whether the Person Filing is a

        (a) [ ] Broker or Dealer registered under Section 15 of the Act 
(15 U.S.C. 78o);

        (b) [ ] Bank as defined in section 3(a)(6) of the Act (15 U.S.C. 78c);

        (c) [ ] Insurance company as defined in section 3(a)(19) of the Act 
(15 U.S.C. 78c);

        (d) [ ] Investment Company registered under section 8 of the  Investment
Company  Act of  1940 (15 U.S.C. 80a-8);

        (e) [X] An Investment Adviser in accordance with ss.240.13d-1(b)(1)(ii)
(E);

        (f) [ ] An Employee Benefit Plan or Endowment Fund in  accordance   with
ss.240.13d-1(b)(1)(ii)(F);

        (g) [ ] A Parent Holding Company or control person in accordance with 
ss.240.13d-1(b)(1)(ii)(G);



        (h) [ ] A Savings   Associations  as   defined in  Section  3(b) of  the
Federal  Deposit  Insurance  Act (12 U.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 Company Act of 1940
(15 U.S.C. 80a-3);

        (j) [ ] Group, in accordance with ss.240.13d-1(b)(1)(ii)(J).


Item 4.  Ownership

         (a)    Amount Beneficially Owned (as of December 31, 1998):

                222,141 (all such shares the reporting person has the right to
                acquire upon  conversion of convertible  securities  issued by
                the Issuer)

         (b)    Percent of Class (as of December 31, 1998):

                1.0%                                                         

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

               (i) sole power to vote or to direct the vote   222,141

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

             (iii) sole power to dispose or to direct the disposition of 222,141

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


Item 5.  Ownership of Five Percent or Less of a Class

         If this statement is being filed to report the fact that as of the date
hereof the reporting  person has ceased to be the beneficial  owner of more than
five percent of the class of securities, check the following [ X ].

Item 6.  Ownership of More Than Five Percent on Behalf of Another Person

         The shares of the Issuer beneficially owned by the reporting person are
held on behalf of the  reporting  person's  clients in  accounts  over which the
reporting  person has complete  investment  discretion.  No other person has the
right to receive or the power to direct the receipt of  dividends  from,  or the
proceeds from the sale of, such shares.  No other person's  interest  relates to
more than five percent of the class.  No client account  contains more than five
percent of the class.

Item 7.  Identification  and  Classification of the Subsidiary Which Acquired 
the Security Being Reported on by the Parent Holding Company.  N/A

Item 8.  Identification and Classification of Members of the Group.  N/A




Item 9.  Notice of Dissolution of Group.  N/A

Item 10. Certification

         By  signing  below I  certify  that,  to the best of my  knowledge  and
belief,  the  securities  referred  to above were  acquired  and are 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 and are not held in  connection
with or as a participant in any transaction having that purpose or effect.

                                    SIGNATURE


         After reasonable  inquiry and to the best of my knowledge and belief, I
certify that the information  set forth in this statement is true,  complete and
correct.



                                                     January 29, 1999      
                                                        (Date)



                                                     /s/ Steven E. Berman  
                                                       (Signature)



                                                     Steven E. Berman/Member
                                                         (Name/Title)


      Attention: Intentional misstatements or omissions of fact constitute
                Federal criminal violations (See 18 U.S.C. 1001)