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 stage 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 computed tomography (CT) scan, magnetic resonance imaging (MRI), or calipers by clinical exam. Patients must have newly diagnosed non small cell lung cancer (NSCLC), with no prior overlapping radiation therapy or systemic antineoplastic therapy delivered for locally advanced NSCLC. Prior surgery is allowed. 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 1.5 x institutional upper limit of normal (ULN). (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.) Total bilirubin =< 1.5 x 1.2 mg/dL (ULN). Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase [SGOT])/alanine aminotransferase (ALT)(serum glutamate pyruvate transaminase [SGPT]) =< 2.5 x 39/52 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 ([forced expiratory volume in 1 second] FEV1 > 1.2 liters).  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 cardio toxic 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 base excision repair (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 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 6 months after completion of TRC102 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.  Exclusion Criteria:  Patients who have had prior chemotherapy or overlapping radiotherapy for lung cancer (prior surgery is acceptable). Patients with prior stage I non-small cell lung cancer treated with surgery > 5 years ago are eligible. 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 have not recovered from grade >= 2 adverse events (AEs) due to prior anti-cancer 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.  Current or prior use of immunosuppressive medication within 14 days before the first dose of durvalumab. 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 the first dose of IP. Note: Patients, if enrolled, should not receive live vaccine whilst receiving investigational product (IP) and up to 30 days after the last dose of IP. 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. 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 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 3 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 in >= 5 years before the first dose of 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.