Ipilimumab and Nivolumab in Combination With Radiation Therapy in Treating Patients With Stage 2-3 Non-small Lung Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed NSCLC (any histology) * Patients must have stage II or III local-regionally advanced NSCLC that is deemed to be best treated by systemic and concurrent radiotherapy. Eligible patients with stage II disease must be unresectable or refuse surgical resection * No prior therapy for the current stage II or stage III NSCLC disease * ECOG (Eastern Cooperative Oncology Group) performance status =\< 2 (Karnofsky \>= 60%) * Leukocytes \>= 2,000/mcL * Absolute neutrophil count \>= 1,000/mcL * Platelets \>= 75,000/mcL * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) =\< 3 x institutional ULN * Creatinine =\< 1.5 x institutional ULN * Glomerular filtration rate (GFR) \>= 50 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * No prior history of autoimmune disease, including but not limited to systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, vascular thrombosis associated with antiphospholipid syndrome, Wegener's granulomatosis, Sjogren's syndrome, Bell's palsy, Guillain-Barre syndrome, multiple sclerosis, autoimmune vasculitis, or glomerulonephritis * Patients with a history of autoimmune hypothyroidism on a stable dose of thyroid replacement hormone may be eligible * Patients with controlled type 1 diabetes mellitus on a stable insulin regimen may be eligible * Patients with eczema, psoriasis, lichen simplex chronicus of vitiligo with dermatologic manifestations only (e.g., patients with psoriatic arthritis would be excluded) are permitted provided that they meet the following conditions: * Patients with psoriasis must have a baseline ophthalmologic exam to rule out ocular manifestations * Rash must cover less than 10% of body surface area (BSA) * Disease is well controlled at baseline and only requiring low potency topical steroids (e.g., hydrocortisone 2.5%, hydrocortisone butyrate 0.1%, fluocinolone 0.01%, desonide 0.05%, alclometasone dipropionate 0.05%) * No acute exacerbations of underlying condition within the last 12 months (not requiring PUVA \[psoralen plus ultraviolet A radiation\], methotrexate, retinoids, biologic agents, oral calcineurin inhibitors, high potency or oral steroids) * No prior history of idiopathic pulmonary fibrosis, pneumonitis (including drug induced), organizing pneumonia (i.e., bronchiolitis obliterans, cryptogenic organizing pneumonia, etc.), or evidence of active pneumonitis on screening chest computerized tomography (CT) scan * No active pregnancy. The effects of ipilimumab-nivolumab on the developing human fetus are unknown. For this reason and because radiation and possibly immunotherapies used in this trial are known or possibly known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 7 months after completion of ipilimumab-nivolumab administration * Ability to understand and the willingness to sign a written informed consent document * Patients with known epidermal growth factor receptor (EGFR) mutation or anaplastic lymphoma kinase (ALK) rearrangement are eligible Exclusion Criteria: * Prior systemic therapy for the current active local-regionally advanced NSCLC * Patients who are receiving any other investigational agents * History of allergic reactions attributed to compounds of similar chemical or biologic composition to nivolumab * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study because nivolumab is an immunotherapy agent with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with nivolumab, breastfeeding should be discontinued if the mother is treated with nivolumab. These potential risks may also apply to radiation therapy used in this study * Known human immunodeficiency virus (HIV) positivity * Active chronic treatment (that is still required) with systemic immunosuppressive medications (including but not limited to prednisone, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor \[TNF\] agents) * Patients who have received acute, low dose, systemic immunosuppressant medications (e.g., a one-time dose of dexamethasone for nausea) may be enrolled. The use of inhaled corticosteroids and mineralocorticoids (e.g., fludrocortisone) for patients with orthostatic hypotension or adrenocortical insufficiency is allowed * History of severe allergic, anaphylactic, or other hypersensitivity reactions to chimeric or humanized antibodies or fusion proteins * Patients with prior allogeneic bone marrow transplantation or prior solid organ transplantation * Active untreated hepatitis. Patients with known past or resolved hepatitis B infection (defined as having a negative hepatitis B surface antigen \[HBsAg\] test and a positive anti-HBc \[antibody to hepatitis B core antigen\] antibody test) are eligible. Patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV RNA (ribonucleic acid). Hepatitis B virus (HBV) and HCV viral loads must also be undetectable * Known active untreated tuberculosis * Administration of a live, attenuated vaccine within 4 weeks before treatment start or anticipation that such a live attenuated vaccine will be required during the study. Influenza vaccination should be given during influenza season only (approximately October to March). Patients must not receive live, attenuated influenza vaccine (e.g., FluMist) within 4 weeks prior to treatment start or at any time during the study * Malignancies within 3 years prior to treatment start, with the exception of those with a negligible risk of metastasis or death and with expected curative outcome (such as adequately treated stage I-II cancers, carcinoma in situ of the cervix, basal or squamous cell skin cancer, localized prostate cancer treated surgically with curative intent, or ductal carcinoma in situ treated surgically with curative intent) or undergoing active surveillance per standard-of-care management (e.g., CLL \[chronic lymphocytic leukemia\] Rai stage 0, prostate cancer with Gleason score =\< 6, and prostate-specific antigen \[PSA\] =\< 10 mg/mL, etc.)