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 bil…