<PAGE>
 
                                                                   EXHIBIT 10.56


                          LIFE MEDICAL SCIENCES, INC.
                             STOCK OPTION AGREEMENT
             UNDER THE AMENDED AND RESTATED 1992 STOCK OPTION PLAN
                          (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 under the Company's Amended and Restated 1992 Stock Option Plan (the
"Plan") to acquire shares of the Company's Common Stock, $.001 par value (the
"Shares"); and

  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.
      -------------------------------------- 

      Subject to Section 4 hereof, the Option shall vest and become exercisable
on the dates and as to the installment amounts set forth on the signature page
to this Agreement. To the extent the Option (or any portion thereof) is not
exercised by the Optionee when it becomes exercisable, it shall not expire, but
shall be carried forward and shall be exercisable, on a cumulative basis, until
the Expiration Date (as hereinafter defined) or until earlier termination as
hereinafter provided.
<PAGE>
 
  4.  Term; Extent of Exercisability.
      ------------------------------ 

      (a) Term.

          (i)    The Option shall expire as to each installment amount on the
          date set forth next to each such amount on the signature page to this
          Agreement (the "Expiration Date"), subject to earlier termination as
          herein provided.

          (ii)   Except as otherwise provided in this Section 4, if the Optionee
          ceases to perform services for the Company, the Option shall terminate
          on the earlier of the last day of the third month or ninety days after
          the date such Optionee ceases to perform services for the Company, or
          on the date on which the Option expires by its terms, whichever occurs
          first.

          (iii)  If such termination to perform services is because of dismissal
          for cause or because the Optionee is in breach of any employment
          agreement, such Option will terminate on the date the Optionee ceases
          to perform services for the Company.

          (iv)   If such termination to perform services is because the Optionee
          has become permanently disabled (within the meaning of Section
          22(e)(3) of the Code), such Option shall terminate on the last day of
          the twelfth month from the date such Optionee ceases to perform
          services for the Company, or on the date on which the Option expires
          by its terms, whichever occurs first.

          (v)    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.

     (b)  Extent of Exercisability.
          ------------------------ 

          (i)    Except as provided below, if the Optionee ceases to perform
          services for the Company, the Option shall be exercisable only to the
          extent that the right to purchase Shares under such Option has accrued
          and is in effect on the date such Optionee ceases to perform services
          for the Company.

          (ii)   If the Optionee ceases to perform services for the Company
          because he or she has become permanently disabled (within the meaning
          of Section 22(e)(3) of the Code), the Option shall be exercisable to
          the full number of Shares covered by such Option.

                                      -2-
<PAGE>
 
          (iii)  In the event of the death of the Optionee, the Option may be
          exercised with respect to the full number of Shares covered thereby
          whether or not under the provisions of Section 3 hereof the Optionee
          was entitled to do so at the date of his or her death, by the estate
          of such Optionee, or by any person or persons who acquired the right
          to exercise such Option by bequest or inheritance or by reason of the
          death of such Optionee.

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

     (a)  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
     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 ninety (90) days from the date of receipt of the notice by the
     Company.

     (b)  The Company shall at all times during the term of the Option reserve
     and keep available such number of Shares of its Common Stock as will be
     sufficient to satisfy the requirements of the Option.

  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 or 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 the bankruptcy
of the Optionee or 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.

  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 

                                      -3-
<PAGE>
 
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 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 Optionee's 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 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.

                                      -4-
<PAGE>
 
  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 superseded 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 1st day of
July, 1998.

                              LIFE MEDICAL SCIENCES, INC.



                              By:  /s/ Robert G. Conway
                                  -------------------------------------------


                              OPTIONEE


                              Print Name:    Robert G. Conway
                                         ------------------------------------

                              Sign Name:     /s/ Robert G. Conway
                                         ------------------------------------


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

Total Number of Shares Underlying Option:  75,000
Purchase Price Per Share:        $ 1.40

                         VESTING & EXPIRATION SCHEDULE
                         -----------------------------
 
Vesting Date                    Number of Shares                Expiration Date
------------                    ----------------                ---------------
July 1, 1998                        25,000                        July 1, 2005
July 1, 1999                        25,000                        July 1, 2006
July 1, 2000                        25,000                        July 1, 2007

                                      -5-
<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 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."

                                      -6-
<PAGE>
 
     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,


                              /s/ Robert G. Conway


Dated: _____________

                                      -7-
<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:



                                             /s/ R. G. Conway
                              ------------------------------------------------- 
                                                (Signature)


                                             Robert G. Conway
                              ------------------------------------------------- 
                                               (Print Name)

                                      -8-