Maintenance Chemotherapy With or Without Local Consolidative Therapy in Treating Patients With Stage IV Non-small Cell Lung Cancer

Inclusion Criteria: * Patients must have the psychological ability and general health that permits completion of the study requirements and required follow up * Women of childbearing potential and men who are sexually active should be willing and able to use medically acceptable forms of contraception during the trial and for up to 180 days after completion of all treatment to prevent pregnancy or fathering a child. * Pathologically proven diagnosis of NSCLC, with metastases (stage IV disease) present prior to registration; this includes patients newly diagnosed with metastatic disease or those initially diagnosed and treated for stage I-III NSCLC who ultimately develop limited metastases. Limited metastases is defined as 3 or fewer sites of metastatic disease * Appropriate stage for study entry based on the following diagnostic workup: * History/physical examination by a radiation oncologist (and a surgeon if surgery is planned) within 30 days prior to registration * Imaging proof of limited metastatic disease and response to therapy/stable disease, by at least diagnostic quality CT chest through the adrenals or positron emission tomography (PET)/CT within 30 days prior to registration * Zubrod performance status 0, 1, or 2 within 30 days prior to registration * Adequate organ and hematologic/bone marrow function within 14 days prior to registration, defined as follows: * Aspartate transaminase (AST) and alanine transaminase (ALT) ≤ 2.5 × upper limit of normal (ULN) or ≤ 5 × ULN with metastatic liver disease * Total bilirubin ≤ 1.5 × ULN * Absolute neutrophil count (ANC) ≥ 500 cells/mm3 * Platelets ≥ 50,000 cells/mm3 * Renal: * Creatinine ≤ 1.5 x ULN; or * Creatinine Clearance (CrCl) \> 45 mL/min if creatinine \> 1.5 x ULN (calculated CrCl based on Cockcroft-Gault equation) * HIV-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial. * For patients who will undergo resection of disease (if randomized to Arm 2 and dispositioned to receive surgery), adequate pre-surgical work-up for anticipated surgery, as defined by institutional guidelines. * Negative serum pregnancy test within one week prior to registration for females of childbearing potential * Patients must have received first-line/induction systemic therapy comprising of immunotherapy and/or platinum-based chemotherapy (at least 4 cycles or courses but less than 6, i.e. 4-5 cycles/courses), and achieved stable disease or a partial response. Though the intention is for every course/cycle to be identical in an induction regimen, Some but not all of the 4-5 cycles may omit an immunotherapy or platinum compound if the treating physician determines it is in the patient's best interest secondary to toxicity or other institutional parameter. * For patients treated with nivolumab, ipilimumab and 2 cycles of chemotherapy, the 4-5 cycles requirement will be met by 4-5 total doses of nivolumab. * For patients treated with nivolumab and ipilimumab, this requirement will be met by 2 doses of ipilimumab and 4-5 doses of nivolumab. * After induction systemic therapy, patients must have a minimum of one site of disease, primary or metastasis, present for potential consolidation with local therapy. All sites of disease present after induction systemic therapy, primary and metastases (up to 3) are able to be consolidated with local therapy; * Prior systemic therapy as part of concurrent treatment approach for previously diagnosed stage I-III NSCLC, adjuvant or neo-adjuvant therapy for stage I-III NSCLC, as adjuvant therapy for previously resected or irradiated NSCLC, or for other previous cancers is permitted * For de novo stage IV NSCLC patients (patients with metastatic disease at first presentation), primary disease must be treatable with local therapy in the form of SBRT or hypofractionated radiation. If the primary disease is found in the peripheral or central lung parenchyma without nodal disease, for instance, SBRT may be employed at the discretion of the treating institution. If primary disease is more advanced with involvement of the mediastinum (T4 tumor, N1-N3 disease, etc.), these volumes should be technically treatable with hypofractionated radiation; surgery should only be used for metastatic tumors that can be completely resected by lobectomy, segmentectomy, or wide wedge resection. * If primary disease in the thoracic cavity was previously treated with local therapy in the form of surgery or radiation, any new local/regional disease recurrence should be technically treatable with SBRT or hypofractionated radiation after induction systemic therapy. * The patient or a legally authorized representative must provide study-specific informed consent prior to registration. * Radiotherapy for patients with brain metastases prior to registration is acceptable. * Patients with brain metastases are eligible if these lesions have been previously treated or resolved and the patients have no clinical or radiographic evidence of progression prior to registration. * Subjects may receive palliative radiotherapy for symptomatic metastases or primary disease prior to registration provided that there is at least one other non-irradiated lesion amenable to LCT at the time of registration. Exclusion Criteria: * Clinical or radiologic evidence of untreated and/or progressive brain metastases prior to registration after induction systemic therapy * Cutaneous metastasis of NSCLC * Metastatic disease invading the esophagus, stomach, intestines, or mesenteric lymph nodes if not a candidate for surgery for these lesions * Prior invasive malignancy (except non-melanomatous skin cancer, low or intermediate risk prostate cancer, or in situ carcinoma of breast, oral cavity, skin, or cervix) unless disease free for a minimum of one year * Metastases located within 3 cm of previously irradiated (\< 3 Gy per fraction) structures if if not a candidate for surgery for these lesions and if: * Spinal cord previously irradiated to \> 40 Gy * Brachial plexus previously irradiated to \> 50 Gy * Small intestine, large intestine, or stomach previously irradiated to \> 45 Gy * Brainstem previously irradiated to \> 50 Gy * Lung previously irradiated with prior V20 Gy \> 35% * Patients receiving targeted therapy (non-cytotoxic systemic therapy) for NSCLC in the first-line setting * Patients with NSCLC who have driver mutations for which targeted therapies (non-cytotoxic, non-immunotherapy based systemic therapy including but not limited to tyrosine-kinase inhibitors) are available. Such designations would include but not be limited to treatments targeting epidermal growth factor receptor (EGFR) mutant or anaplastic lymphoma kinase (ALK) positive NSCLC. * If a patient has progressed in previous areas of primary disease that received definitive doses of radiation, these patients would require re-irradiation in previous high dose anatomic areas and are not eligible for this study. * Patients with malignant pleural effusions that do not resolve after first-line systemic therapy; patients with pleural effusions that have become too small for thoracentesis at the time of registration would be permitted on study, indicating a significant response to first-line systemic therapy * Patients with more than 3 discrete locations of extra-cranial metastatic disease after first-line systemic therapy requiring more than 3 radiation/surgery plans to cover these distinct metastatic disease entities * Acute bacterial or fungal infection requiring intravenous antibiotics at the time of registration * Pregnancy or women of childbearing potential and men who are sexually active and not willing/able to use medically acceptable forms of contraception during treatment and for 180 days after the completion of all treatment. This exclusion is necessary because the treatment involved in this study may be significantly teratogenic. Women who are breastfeeding (and unwilling to discontinue) are also excluded * Participation in any investigational drug study for the treatment of cancer within 4 weeks prior to registration. * For patients who received immunotherapy during induction, patients on chronic steroids or who have active autoimmune disease for which they received systemic treatment in the previous 2 years with corticosteroids, disease modifying agents, or immunosuppressive drugs are not eligible. Replacement therapy (thyroxine, insulin or physiological corticosteroid replacement for adrenal or pituitary insufficiency) is allowed. Patients with active interstitial lung disease or who have a history of pneumonitis for which they had received glucocorticoids are not eligible * Use of bevacizumab or other antiangiogenic therapy in first-line or planned maintenance therapy (due to potential for increased complications from local therapy