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

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) - American College of Radiology Imaging Network (ACRIN) performance status 0-2

Measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1

Fasting blood glucose (FBS) =\< 130 and hemoglobin A1C (HGBA1C) =\< 8.0% and fasting triglycerides =\< 300 mg/dL

Tissue accessible for fine needle and/or core needle biopsy for molecular testing (for expansion cohorts only)

Absolute neutrophil count \>= 1,500/mcL

Platelets \>= 100,000/mcL

Total bilirubin =\< 1.5 x upper limit of normal (ULN)

Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x ULN (=\< 5 x ULN if liver metastases are present)

Creatinine =\< 1.3 mg/dL OR

Glomerular filtration rate (GFR) \>= 40 mL/min/1.73 m\^2

Hemoglobin \>= 9 g/dL (without transfusion within 1 week preceding study drug administration)

For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated

Because no dosing or adverse event data are currently available on the use of CB-839 HCl (telaglenastat) in combination with MLN0128 (sapanisertib) in patients \< 18 years of age, children are excluded from this study, but will be eligible for future pediatric trials

Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial

Females of childbearing potential must have a negative pregnancy test (=\< 14 days) prior to start of trial treatment

* Females who:

* Are postmenopausal for at least 1 year before the screening visit, OR

* Are surgically sterile, OR

* If they are of childbearing potential, agree to practice 1 effective method of contraception and 1 additional effective (barrier) method, at the same time, from the time of signing the informed consent through 90 days (or longer as mandated by local labeling \[e.g. USPI, SmPC, etc\]) after the last dose of study drug, OR

* Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the patient (Periodic abstinence \[e.g. calendar, ovulation, symptothermal postovulation methods\], withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception. Female and male condoms should not be used together)

* Agree not to donate egg(s) during the course of this study or within 90 days after receiving their last dose of study drug

* Male patients, even if surgically sterilized (i.e. status post vasectomy), must agree to the following contraceptive requirements:

* Agree to practice highly effective barrier contraception during the entire study treatment period and through 120 days after the last dose of study drug, OR

* Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the patient (Periodic abstinence \[e.g. calendar, ovulation, symptothermal postovulation methods\], withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception. Female and male condoms should not be used together)

* Agree not to donate sperm during the course of this study or within 120 days after receiving their last dose of study drug

* The effects of CB-839 HCl (telaglenastat) and MLN0128 (sapanisertib) on the developing human fetus are unknown. For this reason, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of CB-839 HCl (telaglenastat) administration

Ability to understand and the willingness to sign a written informed consent document. Participants with impaired decision-making capacity (IDMC) who have a legally-authorized representative (LAR) and/or family member available will also be eligible

What this study is about