Testing the Safety of Adding Either Monalizumab (IPH2201) or Oleclumab (MEDI9447) to Durvalumab (MEDI4736) Plus Standard Radiation Therapy for Locally Advanced Non-small Cell Lung Cancer (NSCLC), ARCHON-1 Trial

Inclusion Criteria: * Pathologic (cytological or histological) proof of diagnosis of stage II-III (American Joint Committee on Cancer \[AJCC\] 8th edition \[ed.\]) unresectable or inoperable, non-metastatic non-small cell lung cancer (NSCLC) within 60 days prior to registration, with no liver or renal end organ damage, as determined by normal laboratory values noted below. Locally recurrent, N1-N3 disease following surgery without prior radiation therapy is eligible. Patients with N1 to N3 and undetectable primary lung tumors (T0) are eligible * Pathological diagnosis of PD-L1 high expressing tumors (\>= 50%) within 60 days prior to registration (using Dako 22C3 immunohistochemistry \[IHC\] antibody or the Ventana SP263 antibody platforms) performed at a Clinical Laboratory Improvement Act (CLIA)-certified lab * Appropriate stage for study entry based on the following diagnostic workup: * History/physical examination within 30 days prior to registration; * Positron emission tomography (PET)/computed tomography (CT) scan for staging within 30 days prior to registration (note: if CT portion of PET/CT scan is not of diagnostic quality, then a separate CT scan with contrast is required); * Magnetic resonance imaging (MRI) scan of the brain with contrast; if medically contraindicated, then CT scan of the brain with contrast (unless medically contraindicated) is acceptable, within 30 days prior to registration; * Sufficient lung function with forced expiratory volume in 1 second (FEV1) \>= 0.8 liter or \>= 35% predicted and carbon monoxide diffusing capability (DLCO) \>= 40% with or without bronchodilator within 30 days prior to registration; * Patients who meet the criterion above without oxygen (O2), but who need acute (started within 10 days prior to registration) supplemental oxygen due to tumor-caused obstruction/hypoxia are eligible, provided the amount of the O2 needed has been stable * Age ≥ 18 * Minimum body weight \>= 40 kg * Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 within 30 days prior to registration * Absolute neutrophil count (ANC) \>= 1500 cells/mm\^3 (within 30 days prior to registration) * Lymphocyte count \>= 500 cells/mm\^3 (within 30 days prior to registration) * Platelet count \>= 100,000 cells/mm\^3 (within 30 days prior to registration) * Hemoglobin \>= 9.0 g/dL (within 30 days prior to registration) (Note: The use of transfusion or other intervention to achieve hemoglobin \[Hgb\] \>= 9.0 g/dl is acceptable) * Creatinine clearance \>= 40 mL/min by the Cockcroft-Gault (C-G) equation * Total bilirubin =\< 1.5 x upper limit of normal (ULN) with the following exception (within 30 days prior to registration): * Patients with known Gilbert disease who have serum bilirubin level =\< 3 x ULN may be enrolled * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 x ULN (within 30 days prior to registration) * Evidence of post-menopausal status or negative urinary or serum pregnancy test for female pre-menopausal patients, obtained within 14 days prior to registration. Women will be considered post-menopausal if they have been amenorrheic for 12 months without an alternative medical cause. The following age-specific requirements apply: * Women \< 50 years of age would be considered post-menopausal if they have been amenorrheic for 12 months or more following cessation of exogenous hormonal treatments and if they have luteinizing hormone and follicle-stimulating hormone levels in the post-menopausal range for the institution or underwent surgical sterilization (bilateral oophorectomy or hysterectomy) * Women \>= 50 years of age would be considered post-menopausal if they have been amenorrheic for 12 months or more following cessation of all exogenous hormonal treatments, had radiation-induced menopause with last menses \> 1 year ago, had chemotherapy-induced menopause with last menses \> 1 year ago, or underwent surgical sterilization (bilateral oophorectomy, bilateral salpingectomy or hysterectomy) * Patients who are human immunodeficiency virus (HIV) positive may participate IF they meet the following eligibility requirements: * They must be stable on their anti-retroviral regimen, and they must be healthy from an HIV perspective * They must have a CD4 count of greater than 250 cells/mcL * They must not be receiving prophylactic therapy for an opportunistic infection * The patient or a legally authorized representative must provide study-specific informed consent prior to study entry Exclusion Criteria: * Definitive clinical or radiologic evidence of metastatic disease * Prior invasive malignancy (except those with a negligible risk of metastasis or death and with expected curative outcome \[such as adequately treated carcinoma in situ of the cervix, basal or squamous cell skin cancer, localized prostate cancer treated surgically with curative intent, or ductal carcinoma in situ treated surgically with curative intent\] or undergoing active surveillance per standard-of-care management \[e.g., chronic lymphocytic leukemia (CLL) Rai stage 0, prostate cancer with Gleason score =\< 6, and prostate specific antigen (PSA) =\< 10 mg/mL\]) unless disease free for a minimum of 3 years * Prior chemotherapy or systemic therapy for the study cancer; note that prior chemotherapy for a different cancer is allowable * Prior radiotherapy to the region of the study cancer that would result in overlap of radiation therapy fields so that cumulative composite dose combining previous plan and current plan to be within 80 Gy to the trachea, major blood vessels, esophagus, and heart, and 55 Gy to the spinal cord (if such patients are being considered, this will need to be centrally reviewed). Prior chest radiation without overlap is permissible * Prior history of myocardial infarction, stroke, or transient ischemic attack in the past 3 months * 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, Guillain-Barre syndrome, multiple sclerosis, vasculitis, or glomerulonephritis. Patients with a history of treated autoimmune thyroid disease requiring thyroid replacement but not immunosuppressives, as well as type 1 diabetes, are permitted. Patients with vitiligo, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger are permitted to enroll * 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 chest PET/CT or CT scan * Severe, active co-morbidity defined as follows: * Known clinically significant liver disease, including active viral, alcoholic, or other hepatitis, cirrhosis, fatty liver, and inherited liver disease; * Any other diseases, metabolic dysfunction, physical examination finding, or clinical laboratory finding giving reasonable suspicion of a disease or condition that contraindicates the use of an investigational drug or that may affect the interpretation of the results or render the patient at high risk from treatment complications; * Active tuberculosis (clinical evaluation that includes clinical history, physical examination and radiographic findings, and tuberculosis \[TB\] testing in line with local practice); * Active hepatitis B (chronic or acute) or hepatitis C infection. Patients with past or resolved hepatitis B infection defined as having a negative hepatitis B surface antigen (HBsAg) test, a positive anti-HBc (antibody to hepatitis B core antigen), and a negative viral deoxyribonucleic acid (DNA) test (only obtained if HBsAg is found positive) are eligible. Patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV ribonucleic acid (RNA) * 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 3 months after the last dose of treatment; this exclusion is necessary because the treatment involved in this study may be significantly teratogenic * Women who are breastfeeding and unwilling to discontinue * Any unresolved toxicity National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) grade \>= 2 from previous anticancer therapy with the exception of alopecia, vitiligo, and the laboratory values defined in the inclusion criteria: * Patients with grade \>= 2 neuropathy will be evaluated on a case-by-case basis after consultation with the study physician. * Patients with irreversible toxicity not reasonably expected to be exacerbated by treatment with durvalumab may be included only after consultation with the study physician * Major surgical procedure (as defined by the investigator) within 28 days prior to registration * Note: * Local surgery of isolated lesions for palliative intent is acceptable * Other major surgery before first dose of immunotherapy is not acceptable * History of allogenic organ transplantation * History of leptomeningeal carcinomatosis * History of active primary immunodeficiency * Current or prior use of immunosuppressive medication within 14 days before registration. (Note: immunosuppressive medication within 14 days before immunotherapy is not acceptable). The following are exceptions to this criterion: * Intranasal, inhaled, topical steroids, or local steroid injections (e.g., intra articular injection); * Systemic corticosteroids at physiologic doses not to exceed \<\<10 mg/day\>\> of prednisone or its equivalent; * Steroids as premedication for hypersensitivity reactions (e.g., CT scan premedication) * Receipt of live attenuated vaccine within 30 days prior to registration * Known allergy or hypersensitivity to any of the study drugs or any of the study drug excipients