Approximately 15 patients with NSCLC who have been treated with multiple prior lines of therapies will be enrolled for Phase 1b. The participants will receive docetaxel (36 mg/m2) intravenous (IV) and MLN1117 tablets, orally administered, once daily in 21-day dosing cycles. The MLN117 dose will be escalated until recommended Phase 2 dose (RP2D) is determined.