Testing the Addition of an Anti-Cancer Drug, TRC102, to the Usual Chemotherapy Treatment (Pemetrexed, Cisplatin or Carboplatin) During Radiation Therapy for Stage III Non-Squamous Non-Small Cell Lung Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed adenocarcinoma or large cell carcinoma of the lung with confirmation by immunohistochemistry (histologic tissue diagnosis is preferred, but cytology is acceptable). * Patients must have newly staged IIIA, IIIB or IIIC disease according to the 8th tumor, node, metastasis (TNM) staging classification and to be considered appropriate candidates for aggressive chemoradiotherapy. * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as \>= 20 mm (\>= 2 cm) by chest x-ray or as \>= 10 mm (\>= 1 cm) with CT scan, MRI, or calipers by clinical exam. * Patients must have diagnosed NSCLC, with no prior overlapping radiation therapy delivered for locally advanced NSCLC. Prior stereotactic radiation therapy for stage I lung cancer without overlapping is allowed. Prior systemic antineoplastic therapy is allowed, as deemed appropriate by the treating physician. Prior surgery is allowed. History of previous stage I NSCLC with new mediastinal nodal recurrence (new stage III are eligible). * Age \>= 18 years. Because no dosing or adverse event data are currently available on the use of TRC102 in combination with pemetrexed, cisplatin, and durvalumab in patients \< 18 years of age, children are excluded from this study. * Body weight \> 30 kg with acceptable nutritional status based on evaluation by treating physician. * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 (Karnofsky \>= 70%). * Leukocytes \>= 3,000/mcL. * Hemoglobin \>= 9.0 g/dL. * Absolute neutrophil count \>= 1,500/mcL. * Platelets \>= 150,000/mcL. * Serum bilirubin within normal institutional limits (0 - 1.2 mg/ dl). (This will not apply to patients with confirmed Gilbert's syndrome \[persistent or recurrent hyperbilirubinemia that is predominantly unconjugated in the absence of hemolysis or hepatic pathology\], who will be allowed only in consultation with their physician.). * Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase \[SGOT\]) =\< 2.5 x institutional upper limit of normal (=\< 39 U/L). * Alanine aminotransferase (ALT)(serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal (=\< 52 U/L). * Creatinine =\< 1.3 mg/dL. * Measured creatinine clearance \>= 60 mL/min OR glomerular filtration rate (GFR) \>= 50 mL/min/1.73 m\^2. * Acceptable pulmonary function as assessed by treating physician. * Evidence of post-menopausal status or negative urinary or serum pregnancy test for female pre-menopausal patients. 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 \< 60 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 \>= 60 years of age will be considered post-menopausal. * Life expectancy \>= 12 months. * 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 with evidence of at least two undetectable viral loads within the past 6 months on the same regimen; the most recent undetectable viral load must be within the past 12 weeks. * They must have a CD4 count of greater than 250 cells/mcL over the past 6 months on this same anti-retroviral regimen and must not have had a CD4 count \< 200 cells/mcL over the past 2 years, unless it was deemed related to the cancer and/or chemotherapy induced bone marrow suppression. * For patients who have received chemotherapy in the past 6 months, a CD4 count \< 250 cells/mcL during chemotherapy is permitted as long as viral loads were undetectable during this same chemotherapy. * They must have an undetectable viral load and a CD4 count \>= 250 cells/mcL within 7 days of enrollment. * They must not be currently receiving prophylactic therapy for an opportunistic infection and must not have had an opportunistic infection within the past 6 months. * HIV-infected patients should be monitored every 12 weeks for viral load and CD4 counts. * For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated. * Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load. * Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association functional classification. To be eligible for this trial, patients should be class 2B or better. * The effects of TRC102 on the developing human fetus are unknown. For this reason and because biochemical inhibitors of the BER pathway agents as well as other therapeutic agents used in this trial are 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, for the duration of study participation, and for 6 months after completion of durvalumab monotherapy. 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 6 months after completion of durvalumab administration, if having sex with women of childbearing potential. * Ability to understand and the willingness to sign a written informed consent document. Participants with impaired decision-making capacity who have a legally-authorized representative (LAR) and/or family member available will also be eligible. * Patients with prior stage I/II non-small cell lung cancer treated with surgery are eligible. Patients with prior stage I NSCLC treated with stereotactic body radiotherapy (SBRT) without overlapping radiation fields would also be eligible. Patients with prior chemotherapy are eligible, at physician's discretion. Exclusion Criteria: * Patients who have not recovered from adverse events due to prior anti-cancer therapy (i.e., have residual toxicities \> grade 1) with the exception of alopecia. * Patients who are receiving any other investigational agents. * Patients with treated brain metastases are not eligible as the study is for stage III disease only. * Patients with new or progressive brain metastases (active brain metastases) or leptomeningeal disease are not eligible as the study includes only stage III disease. * Patients with EGFR or ALK mutations are ineligible. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to TRC102 or other agents used in study. * Patients with uncontrolled intercurrent illness, including but not limited to, ongoing or active infection, symptomatic congestive heart failure, uncontrolled hypertension, unstable angina pectoris, cardiac arrhythmia, interstitial lung disease, serious chronic gastrointestinal conditions associated with diarrhea, or psychiatric illness/social situations that would limit compliance with study requirement, substantially increase risk of incurring adverse events (AEs) or compromise the ability of the patient to give written informed consent. * Patients with psychiatric illness/social situations that would limit compliance with study requirements. * Pregnant women are excluded from this study because TRC102 is a biochemical inhibitor of the BER pathway and durvalumab is an anti-PDL1 antibody, agents 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 TRC102 or durvalumab, breastfeeding should be discontinued if the mother is treated with TRC102 or durvalumab. These potential risks may also apply to other agents used in this study. * 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, for the duration of study participation, and for 6 months after durvalumab monotherapy. 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 6 months after completion of durvalumab. * Patients with active or prior documented autoimmune or inflammatory disorders (including inflammatory bowel disease \[e.g., colitis or Crohn's disease\], diverticulitis \[with the exception of diverticulosis\], systemic lupus erythematosus, sarcoidosis syndrome, or Wegener syndrome \[granulomatosis with polyangiitis, Graves' disease, rheumatoid arthritis, hypophysitis, uveitis, etc.\]). The following are exceptions to this criterion: * Patients with vitiligo or alopecia. * Patients with hypothyroidism (e.g. following Hashimoto thyroiditis) stable on hormone replacement. * Any chronic skin condition that does not require systemic therapy. * Patients without active disease in the last 5 years may be included but only after consultation with the study physician. * Patients with celiac disease controlled by diet alone. * Active infection including tuberculosis (clinical evaluation that includes clinical history, physical examination and radiographic findings, and tuberculosis \[TB\] testing in line with local practice), hepatitis B (known positive HBV surface antigen \[HBsAg\] result), or hepatitis C. Patients with a past or resolved HBV infection (defined as the presence of hepatitis B core antibody \[anti-HBc\] and absence of HBsAg) are eligible. Patients positive for hepatitis C (HCV) antibody are eligible only if polymerase chain reaction is negative for HCV ribonucleic acid (RNA). * History of allogenic organ transplantation. * History of another primary malignancy except for: * Malignancy treated with curative intent and with no active disease before the first dose of investigational product (IP) and of low potential risk for recurrence. * Adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease. * Adequately treated any carcinoma in situ without evidence of disease. * Prostate cancer with stable disease with active or prior treatment that will not interfere with current lung cancer treatment will be eligible.