Cisplatin/Carboplatin and Etoposide With or Without Nivolumab in Treating Patients With Extensive Stage Small Cell Lung Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed extensive stage small cell lung cancer and must be a candidate for systemic therapy; NOTE: The extensive disease SCLC classification for this protocol includes all patients with disease sites not defined as limited stage; limited stage disease category includes patients with disease restricted to one hemithorax with regional lymph node metastases, including hilar, ipsilateral and contralateral mediastinal, and/or ipsilateral supraclavicular nodes; extensive disease patients are defined as those patients with extrathoracic metastatic disease, malignant pleural effusion, bilateral or contralateral supraclavicular adenopathy; patients with locally recurrent SCLC who are not eligible for curative intent chemoradiation are eligible * Patients must have measurable disease based on Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 * Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 * Absolute neutrophil count \>= 1,500/mm\^3 (must be obtained =\< 7 days prior to protocol registration) * Platelets \>= 100,000/mm\^3 (must be obtained =\< 7 days prior to protocol registration) * Leukocytes \>= 3000/mm\^3 (must be obtained =\< 7 days prior to protocol registration) * Hemoglobin \>= 9 g/dL (must be obtained =\< 7 days prior to protocol registration) * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) (except subjects with Gilbert syndrome, who can have total bilirubin \< 3 mg/dL) (must be obtained =\< 7 days prior to protocol registration) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) =\< 3 X institutional upper limit of normal (ULN) (=\< 5 X if liver function test \[LFT\] elevations due to known liver metastases) (must be obtained =\< 7 days prior to protocol registration) * Serum creatinine =\< 1.5 x ULN or calculated creatinine clearance \> 50 mL/min (using the Cockcroft-Gault formula) (must be obtained =\< 7 days prior to protocol registration) * Patients are eligible if central nervous system (CNS) metastases are adequately treated and neurological symptoms have returned to baseline or are controlled for at least 2 weeks prior to enrollment; in addition, subjects must be either off corticosteroids, or on a stable or decreasing dose of =\< 10 mg daily prednisone (or equivalent); patients with untreated CNS metastases are eligible if they are not symptomatic and the lesions are less than 1 cm in size * Patients cannot have had prior chemotherapy or biologic therapy for extensive stage small cell lung cancer for front line treatment; patients receiving prior whole brain radiation cannot register within 7 days after completion of radiation, and must have resolved adverse events attributed to radiation to =\< grade 1; a 1-week washout is permitted for palliative radiation (=\< 2 weeks of radiotherapy) to non-CNS disease * Patients who have received prior chemoradiation treatment with chemotherapy regimen including cisplatin or carboplatin/etoposide for limited-stage SCLC are eligible if treated with curative intent at least 6 months since last treatment from diagnosis of extensive-stage SCLC * Patients may not be receiving any other investigational agents while on study * Women of childbearing potential (WOCBP) and males who are sexually active with WOCBP must use an accepted and effective method of contraception or abstain from sexual intercourse for at least one week prior to the start of treatment, and continue for 5 months after the last dose of protocol treatment for women of childbearing potential and 7 months after the last dose of protocol treatment for males who are sexually active with WOCBP * No prior or current invasive malignancy (except non-melanomatous skin cancer, localized bladder and prostate cancer) unless disease free for a minimum of 2 years (for example, carcinoma in situ of the breast, oral cavity, or cervix are all permissible); * No prior systemic treatment with an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CTLA-4 antibody, or any other antibody or drug specifically targeting T-cell costimulation or immune checkpoint pathways; * No patients with an active, known or suspected autoimmune disease and neuromuscular paraneoplastic syndromes including but not limited to myasthenia gravis, Lambert-Eaton myasthenic syndrome, limbic encephalitis, myositis, Guillain-Barre; subjects with type I diabetes mellitus, hypothyroidism only requiring hormone replacement, skin disorders (such as vitiligo, psoriasis, or alopecia) not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger are permitted to enroll * No patients with a condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalent) or other immunosuppressive medications within 7 days of randomization; inhaled or topical steroids, and adrenal replacement steroid doses \> 10 mg daily prednisone equivalent, are permitted in the absence of active autoimmune disease * No patients with interstitial lung disease that is symptomatic or may interfere with the detection or management of suspected drug-related pulmonary toxicity * No history of severe hypersensitivity reaction to any monoclonal antibody or allergy to study drug components Exclusion Criteria: * Patients must not have history of allergic reactions attributed to compounds of similar chemical or biologic composition to nivolumab or other agents used in the study * Women must not be pregnant or breast-feeding; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with the agents used in this study, breastfeeding must be discontinued or the subject is not eligible for the study; all females of childbearing potential must have a blood test or urine study, with a minimum sensitivity 50 mlU/L or equivalent units of human chorionic gonadotropin (HCG), within 14 days prior to registration to rule out pregnancy; a female of childbearing potential is any woman, regardless of sexual orientation or whether they have undergone tubal ligation, who meets the following criteria: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (i.e. has had menses at any time in the preceding 24 consecutive months) * Patient must not have leptomeningeal disease * Patients must NOT have uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, uncontrolled cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible * Any positive test for hepatitis B virus or hepatitis C virus indicating acute or chronic infection, patients are excluded * Patients are ineligible if they received a live, attenuated vaccine within 4 weeks before randomization