<PAGE>   1
                                                                    EXHIBIT 10.2


                               AMENDMENT OF LEASE



       WHEREAS, N.W.A. Limited Partnership ("Landlord") and ILEX Oncology, Inc.
("Tenant") entered into a Lease dated October 16, 1996 covering certain
Premises in the Northwest Atrium Building (the"Building"); and

       WHEREAS, Tenant wishes to lease additional space in the Building;

       NOW, THEREFORE, in consideration of the premises and other good and
valuable consideration, the receipt and sufficiency of which is hereby
acknowledged, Landlord and Tenant agree as follows:


       1.  PREMISES as defined in the Lease are amended to read as follows:

              Suite No. 300 deemed to contain 21,036 square feet of Rentable
       Area (as hereinafter defined), the same being 18,291 square feet of
       Usable Area (as hereinafter defined); and

              Effective July 1, 1997, Suite 170 deemed to contain 4,810 square
       feet of Rentable Area (as hereinafter defined), the same being 4,183
       square feet of Usable Area (as hereinafter defined).

              Suites 300 and 170 are outlined on the plan attached to this
       Amendment as Exhibit A, and are located in the office building (the
       "Building") located on the land described as, NCB 17442, BLK 1, LOT 1,
       NW Office Park UT-1, Bexar County, Texas and known as Northwest Atrium
       Office Building, 11550 IH010 West (the "Land").


       2.  TERM is amended to read as follows:

              The period of sixty (60) months commencing February 1, 1997 (the
       "Commencement Date") and ending at 5:00 p.m. January 31, 2002 subject to
       adjustment or earlier termination as provided in the Lease.


       3.  BASIC RENTAL is amended to read as follows:

<TABLE>
<CAPTION>
              MONTHLY                      MONTHLY                     MONTHLY
              PERIOD                       BASE RENTAL                 RATE/RSF
              -----------------------------------------------------------------
              <S>                          <C>                         <C>
              1-12
              Thru 6/30/97                 $21,456.72                  $1.02
              7/1/97 - 1/31/98             $26,362.92                  $1.02
              13-24                        $27,655.22                  $1.07
              25-36                        $28,947.52                  $1.12
              37-48                        $30,239.82                  $1.17
              49-60                        $31,532.12                  $1.22
</TABLE>
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       4.  TENANT'S PROPORTIONATE SHARE is amended to read as follows:

              FROM THE COMMENCEMENT DATE THROUGH JUNE 30, 1997:

              22.76% which is the percentage obtained by dividing (I) 21,036
       square feet of Rentable Area in the Premises by (ii) the total 92,410
       square feet of Rentable Area in the Building.

              BEGINNING JULY 1, 1997:

              27.96% which is the percentage obtained by dividing (I) 25,846
       square feet of Rentable Area in the Premises by (ii) the total 92,410
       square feet of Rentable Area in the Building.

       5.  All other terms and conditions of the Lease remain the same.



       Executed this ____ day of _________, 1997.



                                           LANDLORD:

                                           N.W.A. LIMITED PARTNERSHIP



                                           By:
                                              ----------------------------------
                                                  M. Richard Stewart
                                                  Vice President of its
                                                  General Partner
                                                  George Investment Group, Inc.



                                           TENANT:

                                           ILEX Oncology, Inc.





                                           By:
                                              ----------------------------------
                                                  Richard L. Love
                                                  President and Chief Executive
                                                  Officer