In small cell lung cancer (SCLC), acquired resistance to DNA-damaging therapy is challenging to study because rebiopsy is rarely performed. We used patient-derived xenograft models, established before therapy and after progression, to dissect acquired resistance to olaparib plus temozolomide (OT), a promising experimental therapy for relapsed SCLC. These pairs of serial models reveal alterations in both cell cycle kinetics and DNA replication and demonstrate both inter- and intratumoral heterogeneity in mechanisms of resistance. In one model pair, up-regulation of translesion DNA synthesis (TLS) enabled tolerance of OT-induced damage during DNA replication. TLS inhibitors restored sensitivity to OT both in vitro and in vivo, and similar synergistic effects were seen in additional SCLC cell lines. This represents the first described mechanism of acquired resistance to DNA damage in a patient with SCLC and highlights the potential of the serial model approach to investigate and overcome resistance to therapy in SCLC.