Sapanisertib in Treating Patients With Stage IV or Recurrent Lung Cancer

Inclusion Criteria

• •Patients must have histologically or cytologically confirmed stage IV or recurrent squamous cell lung cancer or KRAS mutant lung cancer that harbors any of the NFE2L2 mutations or KEAP1 mutations; any KEAP1 mutation will be eligible
• •Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as \>= 20 mm (\>= 2 cm) with conventional techniques or as \>= 10 mm (\>= 1 cm) with spiral computed tomography (CT) scan, magnetic resonance imaging (MRI), or calipers by clinical exam
• •Patients must have completed at least 1 prior line of systemic therapy; patients who have declined first line therapy or for whom first-line therapy would be clinically inappropriate, will be considered eligible for the trial
• •Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%)
• •Life expectancy of greater than 3 months
• •Leukocytes \>= 3,000/mcL
• •Absolute neutrophil count \>= 1,500/mcL
• •Platelets \>= 100,000/mcL
• •Total bilirubin within normal institutional limits
• •Fasting serum glucose =\< 130 mg/dL or hemoglobin A1C (HBA1C) \< 7.0%
• •Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal
• •Creatinine within normal institutional limits OR creatinine clearance \>= 50 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal
• •Patients with controlled diabetes are allowed on study; controlled diabetes is defined as fetal bovine serum (FBS) =\< 130 mg/dL in the context of this study
• •The effects of MLN0128 (TAK-228) on the developing human fetus are unknown; for this reason women of child-bearing potential and men must agree to practice 1 highly effective method of contraception and 1 additional effective (barrier) method, at the same time, prior to study through 90 days (or longer, as mandated by local labeling \[e.g., United States Package Insert (USPI), Summary of Product Characteristics (SmPC), etc;\]) after the last dose of study drug; 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; any woman who becomes pregnant while receiving MLN0128 (TAK-228) will be removed from the trial; men treated or enrolled on this protocol must also agree to use highly effective barrier contraception prior to the study, for the duration of study participation, and 120 days after completion of MLN0128 (TAK-228) administration; men must agree not to donate sperm during the course of this study or within 120 days after receiving their last dose of study drug
• •Ability to understand and the willingness to sign a written informed consent document
• •Ability to swallow oral medications
• •Known human immunodeficiency virus (HIV) positive patients who meet the following criteria will be considered eligible:
• •* CD4 count \> 350 cells/mm\^3
• •* Undetectable viral load
• •* Maintained on modern therapeutic regimens utilizing non-CYP-interactive agents