Docetaxel With or Without TAK-117 (MLN1117) in Participants With Locally Advanced or Metastatic Non-small Cell Lung Cancer

The drug being evaluated in this study is called TAK-117. TAK-117 is tested in combination with docetaxel versus docetaxel alone for the treatment of non-small cell lung cancer (NSCLC). This study consisted of 2 phases: * Phase 1b - dose escalation phase * Phase 2 - expansion phase. The study enrolled 14 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/m\^2) intravenous (IV) and TAK-117 tablets, orally administered, once daily in 21-day dosing cycles. The TAK-117 dose will be escalated until recommended Phase 2 dose (RP2D) is determined. Each part of the adaptive Phase 2 portion of the study is designed as a stand-alone, randomized study evaluating PFS as the primary efficacy measure in a total of 60 participants between the 2 treatment arms: TAK-117 plus docetaxel versus docetaxel alone. An event-driven analysis of PFS will be performed after each part of Phase 2. On the basis of the PFS analysis of the preceding part of the study, the study may be stopped for efficacy or futility, or proceed to the next part. However, Phase 2 of the study was cancelled. Study drug will be administered in 21-day dosing cycles. During each phase of the study, participants will be treated with a maximum of 9 cycles of either docetaxel alone or docetaxel plus TAK-117. Subsequently, participants treated with docetaxel plus TAK-117 may continue to receive TAK-117 monotherapy until progression of disease, occurrence of unacceptable toxicities or death. The maximum duration of treatment for participants will be 12 months unless it is determined that a participant would derive benefit from continued treatment beyond 12 months. Participants will continue to be followed after discontinuation of study drug to collect PFS and OS data. Participants may withdraw from therapy at any time. This multicenter trial will be conducted in North America. The overall time to participate in this study is up to 24 months.