Background: Lesch–Nyhan syndrome (LNS) is a rare X-linked recessive metabolic disorder caused by mutations in the HPRT1 gene, resulting in hypoxanthine–guanine phosphoribosyltransferase (HPRT) deficiency. Early diagnosis is critical for optimizing management and improving outcomes. This study presents a case series of three Taiwanese patients diagnosed at a single medical center. Methods: Exome sequencing and biochemical testing were used to confirm the diagnoses. Early clinical manifestations, including hyperuricemia, hypotonia, and developmental delay, were documented during the initial stages of the disease. Results: All three patients had hyperuricemia, hypotonia, spasticity, and motor developmental delay. Pathogenic variants in the HPRT1 gene were identified in two patients, while the third was confirmed by biochemical testing. Two patients had orange-colored crystalline deposits in their diapers, indicative of hyperuricosuria. Self-injurious behavior had not yet developed in two patients due to their young age. Conclusions: Early clinical features such as hyperuricemia, hypotonia, and motor delay may suggest LNS in infancy. Molecular genetic testing, particularly whole exome sequencing, can facilitate an early diagnosis before specific manifestations occur, enabling timely interventions and improving patient outcomes.