Nivolumab and Metformin Hydrochloride in Treating Patients With Stage III-IV Non-small Cell Lung Cancer That Cannot Be Removed by Surgery

Inclusion Criteria: * Patients must have histologically confirmed, locally advanced or metastatic stage IV or non-resectable stage III non-small cell lung cancer (NSCLC) * Patients may have received any number and type of prior treatment regimens for their NSCLC (aside from patients in arm A, who cannot have had PD-1/PD-L1 inhibitors) * Arm A: patients must be treatment naive to single agent PD-1/PD-L1 inhibitors including but not limited to durvalumab, pembrolizumab, atezolizumab, nivolumab, and avelumab * Arm B: patients' tumor must be either refractory to or progressed on one of the above agents * Both cases are defined by initial progressive disease (PD) or PD after CR, PR, or SD using RECIST criteria, respectively * Patients must have measurable disease according to the standard RECIST version 1.1 * NOTE: computed tomography (CT) scans or magnetic resonance imaging (MRI)s used to assess the measurable disease must have been completed with 28 days prior to the study drug initiation * Patients need to have adequate kidney, bone marrow, and liver functions =\< 14 days of registration as specified below: * Absolute neutrophil \>= 1,000/mcL; transfusion and/or growth factor are permitted within any timeframe * Platelets \>= 50,000/mcl; transfusion and/or growth factor are permitted within any timeframe * Total bilirubin =\< 1.5 times the institutional upper limit of normal (ULN) (or =\< 3 times ULN in case of liver metastasis or Gilbert syndrome) * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SPGT\]) =\< 2.5 X institutional ULN (or =\< 5 times ULN in case of liver metastasis) * Creatinine =\< 1.4 ng/mL for females; =\< 1.5 ng/mL for males; patients with creatinine =\< 2.0 ng/mL may still be eligible if in the opinion of the investigator, the benefits of treatment outweigh the risks * Patients must exhibit an Eastern Cooperative Oncology Group (ECOG) performance status of =\< 2 * Patients must have the ability to understand and the willingness to sign a written informed consent prior to registration on study * Females of child-bearing potential (FOCBP) and men who are sexually active must agree to follow instructions for method(s) of contraception for the duration of treatment and the designated post-treatment period * NOTE: a FOCBP is any woman (regardless of sexual orientation, having undergone a tubal ligation, or remaining celibate by choice) who meets the following criteria: * Has not undergone a hysterectomy or bilateral oophorectomy * Has had menses at any time in the preceding 12 consecutive months (and therefore has not been naturally postmenopausal for \> 12 months) * FOCBP must have a negative pregnancy test =\< 7 days prior to registration on study * Patients with known history of central nervous system (CNS) metastases are eligible if CNS disease has been radiographically and neurologically stable for at least 6 weeks prior to study registration and do not require corticosteroids (of any dose) for symptomatic management * NOTE: CNS imaging is only required at baseline for patients with known history of CNS metastases * Patients must have the ability to swallow oral medications * Patients who are known to be EGFR- or ALK-positive must have received prior EGFR- or ALK-targeted therapy, respectively * NOTE: in such cases, documentation of EGFR mutation or ALK translocation status should be provided if available Exclusion Criteria: * Both arms: patients should not have received metformin within 6 months prior to registration * Arm B: patients who were on metformin while on PD-1/PD-L1 inhibitors are not eligible * Patients should not have received prior immunotherapies (exception; arm B); they include but are not limited to interleukin-2 and other immune checkpoint antagonist targeting CTLA-4, LAG-3, TIM-3, KIR etc. and/or agonists targeting OX40, ICOS, CD137, etc * NOTE: prior cancer vaccine treatments are permitted; for arm B, exposure to single agent PD-1/PD-L1 inhibitors are allowed \>= 14 days from registration * Arm B: patients must not have had prior exposure to combination treatment with PD-1/PD-L1 inhibitors and another systemic treatment * NOTE: radiation therapy and surgery do not count as combination treatment * Patients who are intolerant to PD-1/PD-L1 inhibitors and/or metformin are excluded * Patients with active autoimmune disease or history of autoimmune disease that might recur, which may affect vital organ function or require immune suppressive treatment including chronic prolonged systemic corticosteroids (defined as corticosteroid use of duration one month or greater), should be excluded; these include but are not limited to patients with a history of: * Immune related neurologic disease * Multiple sclerosis * Autoimmune (demyelinating) neuropathy * Guillain-Barre syndrome * Myasthenia gravis * Systemic autoimmune disease such as systemic lupus erythematosus (SLE) * Connective tissue diseases * Scleroderma * Inflammatory bowel disease (IBD) * Crohn's * Ulcerative colitis * Patients with a history of toxic epidermal necrolysis (TEN) * Stevens-Johnson syndrome * Anti-phospholipid syndrome * NOTE: subjects with vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger are permitted to enroll * Patients are ineligible who have any condition requiring systemic treatment with corticosteroids (\> 10 mg daily prednisone equivalents) or other immunosuppressive medications =\< 14 days prior to registration * NOTE: inhaled steroids and adrenal replacement steroid doses \> 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease; a brief (less than 3 weeks) course of corticosteroids for prophylaxis (eg, contrast dye allergy) or for treatment of non-autoimmune conditions (eg, delayed-type hypersensitivity reaction caused by a contact allergen) is permitted * Patients who have an uncontrolled intercurrent illness including, but not limited to any of the following, are not eligible: * Uncontrolled hypertension - blood pressure \>= 150/90 mmHg despite medical therapy * Ongoing or active infection requiring systemic treatment * Symptomatic congestive heart failure * Unstable angina pectoris * Cardiac arrhythmia * Psychiatric illness/social situations that would limit compliance with study requirements * Any other illness or condition that the treating investigator feels would interfere with study compliance or would compromise the patient's safety or study endpoints * Patients must not have had another primary malignancy within 2 years prior to starting study treatment with the exception of adequately treated basal cell carcinoma, squamous cell carcinoma or other non-melanomatous skin cancer, or in-situ carcinoma of the uterine cervix, or any local cancers that are deemed to be cured from investigator's point of view * Patients may not be receiving any other investigational agents =\< 14 days from registration * Patients with known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS) are excluded * Patients who have any positive test for hepatitis B or hepatitis C virus indicating acute or chronic infection are excluded * Patients with known diabetes whose glucose control or general health condition may be adversely affected by the use of metformin as per the study protocol as deemed by either the study investigator or endocrinologist are excluded * Patients must not have any of the following contraindications to metformin: * Hypersensitivity to metformin or any component of the formulation * Kidney dysfunction or abnormal creatinine (Cr \< 2 ng/mL) from any cause * Acute or metabolic acidosis