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