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 categorized by the predominant cell type * STEP 2 ENROLLMENT AND RANDOMIZATION: the patient has a diagnosis of American Joint Committee on Cancer (AJCC) 7th edition stage IV NSCLC * STEP 2 ENROLLMENT AND RANDOMIZATION: completion of 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; note that it is not mandatory to check EGFR mutation or EML4-ALK status prior to entry, but patients that receive options 2 or 3 should have had these molecular tests performed * STEP 2 ENROLLMENT AND RANDOMIZATION: less than or equal to three metastatic lesions and no evidence of disease progression based on RECIST criteria; note that patients that had \> 3 metastatic lesions in Step 1 may be eligible for enrollment in Step 2 if the number of metastatic sites is reduced to three or less * STEP 2 ENROLLMENT AND RANDOMIZATION: the patient's Eastern Cooperative Oncology Group (ECOG) performance status is =\< 2 at study entry * STEP 2 ENROLLMENT AND RANDOMIZATION: absolute neutrophil count (ANC) \>= 1,500/mm\^3 within 3 weeks of study entry * STEP 2 ENROLLMENT AND RANDOMIZATION: platelet count \>= 100,000/mm\^3 within 3 weeks of study entry * STEP 2 ENROLLMENT AND RANDOMIZATION: white blood cells (WBC) \>= 3,000/mm\^3 within 3 weeks of study entry * STEP 2 ENROLLMENT AND RANDOMIZATION: hemoglobin \>= 9 g/dL within 3 weeks of study entry * STEP 2 ENROLLMENT AND RANDOMIZATION: the patient must be a suitable candidate for LCT (radiotherapy and/or surgery) to every site of disease, as determined by the treating physician(s); consultation with a multidisciplinary team, including a medical oncologist, radiation oncologist, and thoracic surgeon, is encouraged but not required * STEP 2 ENROLLMENT AND RANDOMIZATION: concurrent chemoradiation is permitted as consolidative therapy; the following concurrent therapies are permitted: tyrosine kinase inhibitors (i.e. erlotinib) - can be delivered with both hypofractionated (\>= 3 Gray \[Gy\] per fraction) and standard fractionated radiation therapy (\< 3 Gy per fraction); platinum-based chemotherapy - standard fractionated radiation therapy (\< 3 Gy per fraction) * STEP 2 ENROLLMENT AND RANDOMIZATION: bevacizumab will not be permitted within 2 weeks of the initiation of the radiation therapy course * STEP 2 ENROLLMENT AND RANDOMIZATION: treatment to central nervous system lesions, such as the brain or spine (prior to first line systemic therapy), or symptomatic lesions requiring urgent palliative radiation, is permitted prior to randomization, in which case the patient would be randomized to treatment of other metastatic sites or the primary sites (based on the disease remaining after first-line treatment); these treated lesions should be counted towards the total number of metastases at the time of enrollment * STEP 2 ENROLLMENT AND RANDOMIZATION: the patient has signed informed consent * STEP 2 ENROLLMENT AND RANDOMIZATION: women of childbearing potential must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) for the duration of study participation and for six (6) months after discontinuation of the study drugs; childbearing potential will be defined as women who have had menses within the past 12 months, who have not had tubal ligation, hysterectomy or bilateral oophorectomy; should a woman become pregnant or suspect that she is pregnant while participating in this study, she should inform her treating physician immediately; the patient, if a man, agrees to use effective contraception or abstinence for the duration of study participation and for six (6) months after discontinuation of the study drugs Exclusion Criteria: * STEPS 1 AND 2 AND RANDOMIZATION * The patient has a history of uncontrolled angina, arrhythmias, or congestive heart failure * Patients with a history of malignant pleural effusions are not eligible; pleural effusions considered by the investigator too small for a diagnostic thoracentesis are permissible * Patient is pregnant (confirmed by serum beta- b-human chorionic gonadotropin \[HCG\] if applicable) or is breastfeeding * Presence of significant third space fluid which cannot be controlled by drainage