The enzyme deficient in Lesch Nyhan syndrome is:

Ref. Guyton. 13th edition. Page. 879 Lesch-Nyhan syndrome results from a defect in HGPRT, an enzyme involved in the purine salvage pathway. HGPRT catalyzes the conversion of the free base (hypoxanthine of guanine) to a nucleotide (IMP or GMP). HGPRT is not required for de novo purine synthesis, or urate synthesis, or for either the de novo or salvage pathways of pyrimidine metabolism. 
 Features Spastic cerebral palsy
 Self-mutilation (hands, lips)
 Hyperuricemia and gout Early death  X-linked (recessive)