EXHIBIT 32.1

                                  CERTIFICATION

      Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (18 U.S.C. 1350,
as adopted), Arthur T. Sands, M.D., Ph.D., Chief Executive Officer of Lexicon
Genetics Incorporated ("Lexicon"), and Julia P. Gregory, Chief Financial Officer
of Lexicon, each hereby certify that:

      1.    Lexicon's Quarterly Report on Form 10-Q for the period ended
            September 30, 2004, and to which this Certification is attached as
            Exhibit 32.1 (the "Periodic Report"), fully complies with the
            requirements of section 13(a) or section 15(d) of the Securities
            Exchange Act of 1934, and

      2.    The information contained in the Periodic Report fairly presents, in
            all material respects, the financial condition and results of
            operations of Lexicon.

      IN WITNESS WHEREOF, the undersigned have set their hands hereto as of the
1st day of November, 2004.

                                      By:  /s/ Arthur T. Sands
                                         ---------------------------------------
                                           Arthur T. Sands, M.D., Ph.D.
                                           President and Chief Executive Officer

                                      By:  /s/ Julia P. Gregory
                                         ---------------------------------------
                                           Julia P. Gregory
                                           Executive Vice President,
                                           Corporate Development and
                                           Chief Financial Officer