<PAGE>
 
                                                                   EXHIBIT 10.59

                          LIFE MEDICAL SCIENCES, INC.
                            STOCK OPTION AGREEMENT
                                        
                          (non-qualified stock option)
                                        


          AGREEMENT entered into as of the date set forth on the signature page
hereto by and between Life Medical Sciences, Inc., a Delaware corporation, with
a principal place of business at 379 Thornall Street, Edison, New Jersey
(together with its subsidiaries, if any, the "Company"), and the undersigned
(the "Optionee").

     WHEREAS, the Company desires to grant to the Optionee a non-qualified stock
option to acquire shares of the Company's Common Stock, $.001 par value (the
"Shares");

     WHEREAS, the Plan provides that each option is to be evidenced by an option
agreement, setting forth the terms and conditions of the option.

     NOW THEREFORE, in consideration of the premises and of the mutual covenants
and agreements contained herein, the Company and the Optionee hereby agree as
follows:

     1.  Grant of Option.
         --------------- 

     The Company hereby grants to the Optionee a non-qualified stock option
under the Plan (the "Option") to purchase all or any part of an aggregate of the
number of Shares set forth on the signature page to this Agreement on the terms
and conditions hereinafter set forth.  The Option shall NOT be treated as an
incentive stock option under Section 422 of the Internal Revenue Code of 1986.
as amended (the "Code").

     2.  Purchase Price.
         -------------- 

     The purchase price ("Purchase Price") for the Shares covered by the Option
shall be the dollar amount per share set forth on the signature page to this
Agreement.

     3.  Time of Vesting and Exercise of Option.
         -------------------------------------- 

 
          The Option shall vest in full as of March 31, 1999.

     4.      Term
             ----

             a. The Option shall expire as to each installment amount on the
                date set forth next to each such amount on the signature page of
                this Agreement (the "Expiration Date"), subject to earlier
                termination as herein provided.
<PAGE>
 
             b. If such termination to perform services is because of dismissal
                for cause or because the Optionee is in breach of any employment
                or consulting agreement, such Option will terminate on the date
                the Optionee ceases to perform services for the Company.

             c. In the event of the death of the Optionee, the Option granted to
                such Optionee shall terminate on the last day of the twelfth
                month from the date of death, or on the date on which the Option
                expires by its terms, whichever occurs first.

     5.   Manner of Exercise of Option.
          ---------------------------- 

       To the extent that the right to exercise the Option has accrued and is in
     effect, the Option may be exercised in full or in part by giving written
     notice to the Company stating the number of Shares as to which the Option
     is being exercised and accompanied by payment in full for such Shares.  No
     partial exercise may be made for less than one hundred (100) full Shares of
     Common Stock.  Payment shall be made in accordance with the terms of the
     Company's Amended and Restated 1992 Stock Option Plan.  Upon such exercise,
     delivery of a certificate for paid-up, non-assessable Shares shall be made
     at the principal office of the Company to the person exercising the Option,
     not less than thirty (30) and not more than forty-five (45) days from the
     date of receipt of the notice by the Company, but subject to the following
     restriction, which is that the shares will not be registered with the
     Securities Exchange Commission unless and until the Company registers other
     new shares subsequent to the date of this agreement.  Said registration
     will most likely be in conjunction with an equity financing for the
     Company.

     6.   Non-Transferability.
          ------------------- 

       The right of the Optionee to exercise the Option shall not be assignable
     or transferable by the Optionee otherwise than by will or the laws of
     descent and distribution or pursuant to a domestic relations order as
     defined in the Code or Title 1 of the Employee Retirement Income Security
     Act or the rules thereunder, and the Option may be exercised during the
     lifetime of the Optionee only by him or her. The Option shall be null and
     void and without effect upon any attempted assignment or transfer, except
     as herein provided, including without limitation any purported assignment,
     whether voluntary or by operation of law, pledge, hypothecation or other
     disposition contrary to the provisions hereof, or levy of execution,
     attachment, trustee process or similar process, whether legal or equitable,
     upon the Option.
<PAGE>
 
     7.   Representation Letter and Investment Legend.
          ------------------------------------------- 

     In the event that for any reason the Shares to be issued upon exercise of
the Option shall not be effectively registered under the Securities Act of 1933
("1933 Act"), upon any date on which the Option is exercised in whole or in
part, the person exercising the Option shall give a written representation to
the Company in the form attached hereto as Exhibit 1 and the Company shall place
an "investment legend", so-called, as described in Exhibit 1, upon any
certificate for the Shares issued by reason of such exercise.

     8.   Adjustments on Changes in Capitalization
          ----------------------------------------

     Adjustments on changes in capitalization and the like shall be made in
accordance with the provisions of the Company's Amended and Restated 1992 Stock
Option Plan as in effect on the date of this Option.

     9.   No Special Employment Rights.
          ----------------------------

     The provisions of this Section 9 are applicable only to Optionees who
are employees of the Company.  Nothing contained in the Plan or this Option
shall be construed or deemed by any person under any circumstances to bind the
Company to continue the employment of the Optionee for the period within which
this Option may be exercised.  However, during the period of the Optionee's
employment, the Optionee shall render diligently and faithfully the services
which are assigned to the Optionee from time to time by the Board of Directors
or by the executive officers of the Company and shall at no time take any action
which directly or indirectly would be inconsistent with the best interests of
the Company.

     10.  Rights as a Stockholder.
          ----------------------- 

     The Optionee shall have no rights as a stockholder with respect to any
Shares which may be purchased by exercise of this Option unless and until a
certificate or certificates representing such Shares are duly issued and
delivered to the Optionee. Except as otherwise expressly provided in the Plan,
no adjustment shall be made for dividends or other rights for which the record
date is prior to the date such stock certificate is issued.

     11.  Withholding Taxes.
          ----------------- 

     Whenever Shares are to be issued upon exercise of this Option, the Company
shall have the right to require the Optionee to remit to the Company an amount
sufficient to satisfy all Federal, state and local withholding tax requirements
prior to the delivery of any certificate or certificates for the Shares.  The
Company may agree to permit the Optionee to authorize the Company to withhold
Shares of Common Stock purchased upon exercise of the Option to satisfy the
above-mentioned withholding requirement; provided, however, no such agreement
may be
<PAGE>
 
made by an Optionee who is an officer or director within the meaning of Section
16 of the Securities Exchange Act of 1934, as amended, except pursuant to a
standing election to so withhold Shares of Common Stock purchased upon exercise
of the Option, such election to be made in the form set forth in Exhibit 2
hereto and to be made not less than six (6) months prior to such exercise.  Such
election may be revoked only upon providing six (6) months prior written notice
to the Company.

     12.  Plan Provisions Control.
          ----------------------- 

     In the event of any inconsistency between the provisions of this Agreement
and the provisions of the Plan, the inconsistent provision(s) of this Agreement
shall be superceded by the Plan provision(s) to the extent necessary to
reconcile the inconsistency.

     IN WITNESS WHEREOF, the Company has caused this Agreement to be executed,
and the Optionee has hereunto set his or her hand, all as of the 31 day of 
Dec. 1998.

                            LIFE MEDICAL SCIENCES, INC.
                            
                            
                            By:           /s/ DREW KARAZIN 
                                ---------------------------------------
 
                            OPTIONEE:                                           
                                                                                
                            Print Name:    /s/ ROBERT  P. HICKEY                
                                       --------------------------------         
                            
                            Sign Name :   Robert P. Hickey
                                       ------------------------------- 

                               OPTION INFORMATION
                               ------------------

Total Number of Shares Underlying Option: 20,000
Purchase Price Per Share: $.09


                         VESTING & EXPIRATION SCHEDULE
                         -----------------------------

  Vesting Date                  Number of Shares              Expiration Date
  ------------                  ----------------              ---------------
    3/31/99                          20,000                       3/31/06
 
<PAGE>
 
                                   EXHIBIT 1
                           TO STOCK OPTION AGREEMENT
                           -------------------------
Gentlemen:

     In connection with the exercise by me of an option to purchase shares of
Common Stock, $.001 par value, of Life Medical Sciences, Inc. (the "Company'), I
hereby acknowledge that I have been informed as follows:

     1 . The shares of Common Stock of the Company to be issued to me pursuant
to the exercise of said option (the "Shares") have not been registered under the
Securities Act of 1933, as amended (the "Securities Act") and, accordingly, must
be held indefinitely unless the Shares are subsequently registered under the
Securities Act, or an exemption from such registration is available.

     2.  Routine sales of securities made in reliance upon Rule 144 under the
Securities Act can be made only after the holding period provided by that Rule
has been satisfied, and, in any sale to which that Rule is not applicable,
registration or compliance with some other exemption under the Securities Act
will be required.

     3.  The availability of Rule 144 is dependent upon adequate current public
information with respect to the Company being available and, at the time that I
may desire to make a sale pursuant to the Rule, the Company may neither wish nor
be able to comply with such requirement,

     In consideration of the issuance of certificates for the Shares to me, I
hereby represent and warrant that I am acquiring the Shares for my own account
for investment, and that I will not sell, pledge or transfer the Shares in the
absence of an effective registration statement covering the same, except as
permitted by the provisions of Rule 144, if applicable, or some other applicable
exemption under the Securities Act.  In view of this representation and
warranty, I agree that there may be affixed to the certificates for the Shares
to be issued to me, and to all certificates issued hereafter representing the
Shares (until in the opinion of counsel, which opinion must be reasonably
satisfactory in form and substance to counsel for the Company, it is no longer
necessary or required) a legend as follows:

     "The securities represented by this certificate have not been registered
     under the Securities Act of 1933, as amended, and were acquired by the
     registered holder pursuant to a representation and warranty that such
     holder was acquiring the
<PAGE>
 
     Shares for his own account and for investment, with no intention of
     transfer or disposition of the same in violation of the registration
     requirements of that Act.  These securities may not be sold, pledged, or
     transferred in the absence of an effective registration statement under
     such Act, or an opinion of counsel, which opinion is reasonably
     satisfactory to counsel to the Company, to the effect that registration is
     not required under such Act.  "

     I further agree that the Company may place a stop transfer order with its
transfer agent, prohibiting the transfer of the Shares, so long as the legend
remains on the certificates representing the Shares.

                               Very truly yours,



Dated:
      -------------------
<PAGE>
 
                                   EXHIBIT 2
                           TO STOCK OPTION AGREEMENT
                           -------------------------
Gentlemen:

     The undersigned Optionee hereby elects and agrees that, whenever the
undersigned exercises a stock option (including any options which now or may
hereafter be granted), Life Medical Sciences, Inc. (the "Company") shall
withhold from that exercise such number of Shares equal in value to the federal
and state withholding taxes due upon such exercise.  The undersigned further 
acknowledges and agrees that this election may not be revoked without six (6)
months' prior written notice to the Company.

                                   OPTIONEE:


                                   ---------------------------------------------
                                                      (Signature)


                                   ---------------------------------------------
                                                     (Print Name)
<PAGE>
 
[LOGO OF LIFE MEDICAL SCIENCES, INC.]
---------------------------------------------------------------
Improving Life Through Discovery


January 11, 1999

Robert P. Hickey
92 Gooseneck Point Rd.
Oceanport, N.J. 07757

Dear Bob:

Thank you for your participation in our Options in Lieu of Compensation Program
(Program).  This Program represents one of many steps which we have undertaken
to preserve our cash resources.  You will note that the company has increased
the number of options offered to you.  The formula we are using is: number of
options equals dollars forgiven times 1.5 times (1/.375 stock price) or # of
options = $ forgiven x 1.5 x (I/.375 stock price).

Please find attached two originals of the Stock Option Agreement and Exhibit I
for your review and signature.  Please return one signed copy to me for our
records.  Also attached is a copy of the Amended and Restated 1992 Stock Option
Plan for your information.

Please also sign and return one copy of this letter whereby you acknowledge
understanding of and agreement with the following:

1)  In compliance with the terms of the Program, by receipt of this Stock Option
    Agreement for 20,000 shares, you agree to waive your claim to $5,000.00 due
    to you from the Company at 12/31/98.

2)  Participation in the Program is voluntary and at the discretion of the
    Company.  It is the Company's intention to terminate the Program upon
    receipt of additional financing.  Notification of the Program termination
    will be provided.  Termination of the Program in no way effects your rights
    as defined in the Stock Option Agreement.



                                Continued .....

--------------------------------------------------------------------------------
379 Thornall Street . Edison, NJ 08837-2227    TEL 732-494-0440 FAX 732-494-6252
http://www.lifemed.com                                    Email: LMS@lifemed.com