Methoxyamine Hydrochloride, Pemetrexed Disodium, Cisplatin, and Radiation Therapy in Treating Patients With Stage IIIA-IV Non-small Cell Lung Cancer

Inclusion Criteria: * Patients must have pathologic diagnosis of adenocarcinoma or large cell carcinoma of the lung with confirmation by immunohistochemistry (e.g., transcription termination factor 1 \[TTF-1\] positivity) (histologic tissue diagnosis is recommended, but cytology is acceptable); stage IIIA/IIIB or oligometastatic stage IV in which the patient is still considered an appropriate candidate for aggressive chemoradiotherapy for the primary tumor; oligometastatic disease is defined as =\< 5 metastatic sites (=\< 3 lesions per organ); for intracranial metastasis, the patient should have asymptomatic disease that is stable on steroids or 1 to 3 symptomatic metastatic lesions treated with stereotactic radiosurgery (SRS) * Eastern Cooperative Oncology Group (ECOG) performance status \< 2 * Life expectancy of greater than 12 months * Ability to swallow and retain orally-administered medication and does not have any clinically significant gastro-intestinal abnormalities (e.g., malabsorption syndrome or major resection of the stomach or bowel) * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Total bilirubin within normal institutional limits * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) =\< 2.5 x institutional upper limit of normal * Alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal * Creatinine within normal institutional limits OR * Creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Hemoglobin \>= 9 g/dL without transfusion within 7 days prior to enrollment * The effects of methoxyamine (TRC102) on the developing human fetus are unknown; for this reason and because methoxyamine 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 and women treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of methoxyamine administration * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had prior chemotherapy or any other investigational drug within 30 days of registration or prior radiotherapy to the study treatment volume; prior surgery is allowed; there must be at least 6 weeks between mitomycin or nitrosoureas and any new therapy * Patients who are receiving any other investigational agents * Patients with a history of any active malignancy requiring on-going treatment, except basal cell carcinoma or squamous cell carcinoma of the skin * History of allergic reactions attributed to compounds of similar chemical or biologic composition to methoxyamine or to pemetrexed or cisplatin * Undetectable haptoglobin or evidence of glucose-6-phophate dehydrogenase (G6PD) deficiency, pyruvate kinase deficiency, hemoglobinopathy, hereditary spherocytosis, thalassemia or other disorder associated with hemolysis * Patients receiving any medications or substances that are inhibitors or inducers of nonsteroidal anti-inflammatory drugs (NSAIDS), probenecid, salicylates, sulfonamides are ineligible; concomitant drugs that are sensitive CYP450 substrates or strong and moderate CYP450 inducers and inhibitors should be avoided; because the lists of these agents are constantly changing, it is important to regularly consult a frequently-updated list; medical reference texts such as the Physicians' Desk Reference may also provide this information; as part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product * 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 methoxyamine is an 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 methoxyamine, breastfeeding should be discontinued if the mother is treated with methoxyamine; these potential risks may also apply to other agents used in this study * Patients who are known to be human immunodeficiency positive (HIV)-positive and are on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with methoxyamine, pemetrexed or cisplatin; in addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy; appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated