Nivolumab and Ipilimumab With or Without Local Consolidation Therapy in Treating Patients With Stage IV Non-Small Cell Lung Cancer

Inclusion Criteria: * Histologically or cytologically confirmed non-small cell lung cancer; if a diagnostic biopsy is available, a pre-treatment biopsy is not required. Patients with a suspected lung cancer may be consented, but pathology must be confirmed prior to initiating treatment on study. Neuroendocrine carcinomas (e.g. small cell lung cancer \[SCLC\], carcinoid tumors) are not eligible. Carcinomas with neuroendocrine differentiation are eligible. * Stage IV (according to the American Joint Committee on Cancer \[AJCC\] 8th edition) measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1. * Signed and dated written or remote informed consent prior to admission to the study in accordance with International Conference on Harmonization-Good Clinical Practice (ICH-GCP) guidelines and to the local legislation. * For lung adenocarcinoma patients, patients must not harbor any EGFR sensitizing or ALK fusion where there are standard care therapy options available. For patients with histologies other than adenocarcinoma, EGFR and ALK status is not required. Adenocarcinoma patients may be consented prior to the EGFR and ALK status being known, but EGFR and ALK status must be determined prior to initiating therapy. EGFR and ALK status may be determined using either tumor- or plasma-based, Clinical Laboratory Improvement Amendments (CLIA)-certified assays. For patients with non-small cell lung cancer (NSCLC), not otherwise specified (NOS), EGFR/ALK testing is not required, as the frequency of alterations is exceedingly rare in this histology. Also, note that patients with ROS1/RET alterations can be enrolled, as tyrosine kinase inhibitor such as crizotinib aren't established as first line therapy for patients with these alterations. * One prior line of chemotherapy and/or targeted agents for metastatic disease are permitted. This chemotherapy can include maintenance therapy, as long as it was given in the front line setting. In addition, prior antiangiogenic therapy (e.g. bevacizumab) is permitted if used as frontline treatment. Patients must have organ and marrow function as defined below: * Performance status of 0 or 1 if using Eastern Cooperative Oncology Group (ECOG)/Zubrod. * Screening laboratory values must meet the following criteria and should be obtained within 14 days prior to treatment initiation * White blood cell (WBC ) \>= 2000/uL * Neutrophils \>= 1500/uL (obtained within 14 days prior to randomization/registration) * Platelets \>= 100 x 10\^3/uL (obtained within 14 days prior to randomization/registration) * Hemoglobin \> 9.0 g/dL (obtained within 14 days prior to randomization/registration) * Serum creatinine ≤ 1.5 x upper limit of normal (ULN) or creatinine clearance (CrCl) ≥ 50 mL (if using the Cockcroft-Gault formula) * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) ≤ 3 x ULN (obtained within 14 days prior to randomization/registration) * Total Bilirubin ≤ 1.5 x ULN (except subjects with Gilbert syndrome, who can have total bilirubin \< 3.0 mg/dL) (obtained within 14 days prior to randomization/registration) * Women of childbearing potential (WOCBP) must use appropriate method(s) of contraception. Appropriate methods of contraception are as follows. Women will be instructed to adhere to contraception for a period of 26 weeks after the last dose of investigational product. Men receiving nivolumab and who are sexually active with WOCBP will be instructed to adhere to contraception for a period of 35 weeks after the last week of nivolumab/ipilimumab (nivo/ipi). Note: WOCBP is defined as any female who has experienced menarche and who has not yet undergone surgical sterilization (hysterectomy or bilateral oophorectomy) or who is not postmenopausal. Menopause is defined clinically as 12 months of amenorrhea in a woman over 45 in the absence of other biological or physiological causes. In addition, women under the age of 55 must have a documented negative serum or urine test. * Women of childbearing potential must have a negative serum or urine pregnancy test within 48 hours prior to the start of nivolumab. * Men who are sexually active with WOCBP must use any contraceptive method with a failure rate of less than 1% per year. Men receiving nivolumab and who are sexually active with WOCBP will be instructed to adhere to contraception for a period of 35 weeks after the last dose of investigational product. Women who are not of childbearing potential (ie, who are postmenopausal or surgically sterile) as well as azoospermic men do not require contraception. * Subjects with brain metastases are eligible if metastases are adequately treated and subjects are neurologically stable (except for residual signs or symptoms related to the central nervous system \[CNS\] treatment) for at least 2 weeks prior to the first dose of nivolumab. In addition, subjects must be either off corticosteroids, or on a stable or decreasing dose of ≤ 10 mg daily prednisone (or equivalent) for at least 2 weeks prior to the first dose of nivolumab. Patients with asymptomatic, small (e.g. =\< 1 cm) brain metastases are 1) eligible provided that the patient is off corticosteroids, or on a stable or decreasing dose of ≤ 10 mg daily prednisone (or equivalent) for at least 2 weeks prior to the first dose of nivolumab * For cohort 1 subjects may receive radiotherapy for symptomatic metastases prior to enrollment provided that there is at least one other non-irradiated lesion amenable to LCT at the time of enrollment. When feasible, stereotactic body radiation therapy (SBRT) or other hypofractionated techniques are strongly encouraged. Inclusion Criteria In Cohort 2: * Patients must have disease progression per imaging radiologic studies prior to randomization in LONESTAR study (during induction phase) * Patient in this cohort must start therapy with platinum doublet and immune checkpoint inhibitor therapy no longer than 6 weeks after their last day of immune checkpoint inhibitor therapy * Patients must have organ and marrow function as defined below: Performance Status of 0 or 1 if using ECOG/Zubrod. Screening laboratory values must meet the following criteria and should be obtained within 14 days prior to treatment initiation WBC ≥ 2000/μL Neutrophils ≥ 1500/μL Platelets ≥ 100 x103/μL Hemoglobin \> 9.0 g/dL Serum creatinine ≤ 1.5 x ULN or creatinine clearance (CrCl) ≥ 50 mL (if using the Cockcroft-Gault formula below): AST/ALT ≤ 3 x ULN Total Bilirubin ≤ 1.5 x ULN (except subjects with Gilbert Syndrome, who can have total bilirubin \< 3.0 mg/dL) * Women of childbearing potential (WOCBP) must use appropriate method(s) of contraception. Appropriate methods of contraception are as follows. Women will be instructed to adhere to contraception for a period of 26 weeks after the last dose of investigational product. Men receiving nivolumab and who are sexually active with WOCBP will be instructed to adhere to contraception for a period of 35 weeks after the last week of nivo/ipi. Note: WOCBP is defined as any female who has experienced menarche and who has not yet undergone surgical sterilization (hysterectomy or bilateral oophorectomy) or who is not postmenopausal. Menopause is defined clinically as 12 months of amenorrhea in a woman over 45 in the absence of other biological or physiological causes. In addition, women under the age of 55 must have a documented negative serum or urine test. * Women of childbearing potential must have a negative serum or urine pregnancy test within 48 hours prior to the start of therapy. * Men who are sexually active with WOCBP must use any contraceptive method with a failure rate of less than 1% per year. Men receiving nivolumab and who are sexually active with WOCBP will be instructed to adhere to contraception for a period of 35 weeks after the last dose of investigational product Women who are not of childbearing potential (ie, who are postmenopausal or surgically sterile as well as azoospermic men do not require contraception.Subjects with brain metastases are eligible if metastases are adequately treated (exception of ≤1 cm asymptomatic brain metastases, as specified below) and subjects are neurologically stable (except for residual signs or symptoms related to the CNS treatment) for at least 2 weeks prior to the first dose of nivolumab. In addition, subjects must be either off corticosteroids, or on a stable or decreasing dose of ≤ 10 mg daily prednisone (or equivalent) for at least 2 weeks prior to the first dose of nivolumab. In addition, subjects must be either off corticosteroids or on stable or decreasing dose of ≤ 10 mg daily prednisone (or equivalent) for at least 2 weeks prior to the first dose of nivolumab. Patients with asymptomatic, small (e.g. ≤1 cm) brain metastases are eligible and do not require prior local therapy for eligibility, provided that the patient is off corticosteroids, or on a stable or decreasing dose of ≤ 10 mg daily prednisone (or equivalent) for at least 2 weeks prior to the first dose of nivolumab. * Participants enrolled in the cohort 2 must be willing to undergo tumor biopsy prior to the initiation of therapy with immune checkpoint inhibitor and platinum doublet therapy and on treatment biopsies. In cases when such a biopsy is clinically unsafe to perform, archival (meaning obtained at earlier times) tumor biopsies may be accepted the discretion of the study PI. * For cohort 2 subjects may receive radiotherapy for symptomatic metastases at the time of their progression prior to enrollment to cohort 2 Exclusion Criteria: * Systemic immunotherapy for metastatic NSCLC. Immunotherapy agents include, but are not limited to, agents targeting the PD1/PD-L1 axis (e.g. nivolumab, pembrolizumab, atezolizumab, durvalumab) or CTLA-4 (ipilimumab, tremelimumab) pathways. * Any approved anti-cancer therapy, including chemotherapy, or hormonal therapy within 3 weeks prior to the initiation of study treatment. The following exceptions are allowed: hormone-replacement therapy or oral contraceptives * Women must not be breastfeeding. * Patients excluded with any prior treatment of pneumonitis requiring corticosteroids within 60 days prior to the first dose of nivolumab * Unwillingness or inability to follow the procedures required in the protocol. * Any serious or uncontrolled medical disorder that, in the opinion of the investigator, may increase the risk associated with study participation or study drug administration, impair the ability of the subject to receive protocol therapy, or interfere with the interpretation of study results. * Prior malignancy active within the previous 2 years. Patients with locally curable cancers that have been apparently cured, such as basal or squamous cell skin cancer, superficial bladder cancer, or carcinoma in situ of the prostate, cervix, or breast with local control measures (surgery, radiation) are eligible. * Patients should be excluded if they have an active, known or suspected autoimmune disease. Subjects are permitted to enroll if they have vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger. * Patients should be excluded if they have a condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days of study drug administration (i.e. disease-modifying antirheumatic drugs). Inhaled or topical steroids and adrenal replacement doses \> 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease. Note that subjects are permitted to use topical, ocular, intra-articular, intranasal, and inhalational corticosteroids (with minimal systemic absorption). Physiologic replacement doses of systemic corticosteroids are permitted, even if \>10 mg/day prednisone equivalents. A brief course of corticosteroids for prophylaxis (e.g. contrast dye allergy) or for treatment of non-autoimmune conditions (e.g. delayed-type hypersensitivity reaction caused by contact allergen) is permitted. * As there is potential for hepatic toxicity with nivolumab or nivolumab/ipilimumab combinations, drugs with a predisposition to hepatoxicity should be used with caution. * Patients should be excluded if they are known to be positive for hepatitis B virus surface antigen (HBV sAg) or hepatitis C virus ribonucleic acid (HCV antibody) indicating acute or chronic infection. * Patients should be excluded if they have known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS). * History of allergy to study drug components. * History of severe hypersensitivity reaction to any monoclonal antibody. * Prisoners or subjects who are involuntarily incarcerated. * Subjects who are compulsorily detained for treatment of either a psychiatric or physical (infection disease) illness. * Psychological, familial, sociological or geographical factors potentially hampering compliance with the study protocol and follow-up schedule. * Any condition that, in the opinion of the investigator, would interfere with the study treatment or interpretation of the study results.