CPI-613 and Docetaxel in Treating Patients With Stage IIIB or IV Non-small Cell Lung Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed stage IIIB or IV NSCLC with radiographic proof of measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) version (v)1.1 criteria * Eastern Cooperative Oncology Group (ECOG) status of 0 or 1 * Life expectancy of \>= 3 months * Patients must have received previous systemic therapy to include: a regimen of chemotherapy, immunotherapy including anti-PDL or anti-PD-L1 therapies, combined chemotherapy and immunotherapy, provided treatment was discontinued \>= 2 weeks prior to initiation of treatment on the present protocol * Absolute neutrophil count \>= 1,500/uL * Platelets \>= 100,000/uL * Total bilirubin within normal institutional limits * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) within institutional upper limit of normal * International normalized ratio (INR) =\< 1.5 x upper limit of normal (ULN) * Prothrombin time (PT) =\< 1.5 x ULN * Activated partial thromboplastin time (aPTT) =\< 1.5 x ULN or within therapeutic range if receiving anticoagulant therapy OR * Creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * 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 through 30 days after the last dose of study medication; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Ability to understand and the willingness to sign an Institutional Review Board (IRB)-approved informed consent document (either directly or via a legally authorized representative) Exclusion Criteria: * Patients who have had immunotherapy or tyrosine kinase inhibitor (TKI) therapy within two weeks prior to entering the study * Radiotherapy or prior systemic chemotherapy within 2 weeks * Patients who have been treated with more than one chemotherapy regimen, immunotherapy regimen or chemotherapy/immunotherapy regimen for metastatic non-small cell lung cancer * Adverse events resulting from previous therapies have not recovered to grade 1 or less * Patients may not be receiving any other investigational agents * Patients with untreated, symptomatic brain metastases should be excluded from this clinical trial (patients with asymptomatic brain metastases amenable to treatment with Gamma Knife radiosurgery \["GKRS"\] are eligible and may receive GKRS while on protocol) * Lactating females * Patients with EGFR, ALK or ROS-1 mutations who are eligible for treatment with a TKI and who have not received such treatment * History of allergic reactions attributed to compounds of similar chemical or biologic composition to CPI-613 or docetaxel * Uncontrolled intercurrent illness including, but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with CPI-613 * Any condition that may, in the opinion of the investigator, compromise the safety of the patient