Surgery and/or Radiation Therapy or Standard Therapy and/or Clinical Observation in Treating Patients With Previously Treated Stage IV Non-small Cell Lung Cancer

Inclusion Criteria: * STEP 1 ENROLLMENT: the patient has a diagnosis of pathologically confirmed NSCLC by tumor biopsy and/or fine-needle aspiration; mixed tumors will be categorized by the predominant cell type * STEP 1 ENROLLMENT: the patient has a diagnosis of American Joint Committee on Cancer (AJCC) 7th Edition stage IV NSCLC * STEP 1 ENROLLMENT: three or less metastatic lesions (not sites); each lesion (including a satellite nodule) will individually be counted as one, and intrathoracic lymph node involvement (defined here as hilar, mediastinal, or supraclavicular nodes, N1-N3) will collectively be counted as one; in addition, patients can receive treatment to CNS lesions or other symptomatic lesions requiring urgent local therapy prior to randomization, but these lesions will be counted towards the total number after chemotherapy, and patients will only be eligible if there are remaining sites amenable to local therapy after up-front systemic therapy * STEP 1 ENROLLMENT: standard induction chemotherapy planned defined as: at least 4 cycles of platinum doublet chemotherapy for metastatic disease (with or without bevacizumab); if the patient is known to be EGFR mutation positive, erlotinib, afatinib, or gefitinib for \>= 3 months, or for patients with known EML4-ALK fusions, crizotinib for \>= 3 months * STEP 2 ENROLLMENT AND RANDOMIZATION: the patient has a diagnosis of pathologically confirmed NSCLC by tumor biopsy and/or fine-needle aspiration; mixed tumors will be c…