Testing of the Anti Cancer Drugs CB-839 HCl (Telaglenastat) and MLN0128 (Sapanisertib) in Advanced Stage Non-small Cell Lung Cancer

Inclusion Criteria: * Patients must have stage IV or recurrent/metastatic NSCLC and have progressed on or after platinum-based chemotherapy and/or PD-(L)1 immune checkpoint inhibitor. Patients with autoimmune or other conditions where PD-(L)1 checkpoint inhibitors are contraindicated are eligible with progression on or after platinum-based chemotherapy or immunotherapy * Dose escalation: patients with NSCLC known to harbor EGFR, ALK, ROS1, BRAF V600E/K activating mutations must have also progressed on appropriate Food and Drug Administration (FDA)-approved targeted therapies to be eligible for dose escalation * Dose expansion: patients must have stage IV or recurrent/metastatic NSCLC harboring 1) NFE2L2 mutations (LSCC); 2) KEAP1 mutations (LSCC); KRAS/KEAP1 or KRAS/NFE2L2 co-mutations (non-squamous NSCLC); or 3) LSCC WT for NFE2L2 or KEAP1 who have progressed on or after platinum-based chemotherapy and/or PD (L)1 immune checkpoint inhibitors or immunotherapy. Acceptable molecular testing includes Foundation ACT circulating tumor deoxyribonucleic acid (ctDNA) or Guardant 360 ctDNA in plasma or Foundation One or Memorial Sloan Kettering Cancer Center (MSK)-Integrated Mutation Profiling of Actionable Cancer Targets (IMPACT) in tumor tissue. Patients with autoimmune or other conditions where PD-(L)1 checkpoint inhibitors are contraindicated are eligible with progression on or after platinum-based chemotherapy or immunotherapy * Eastern Cooperative Oncology Group (ECOG) - Americ…