Radiation Therapy, Chemotherapy, and Soy Isoflavones in Treating Patients With Stage IIIA-IIIB Non-Small Cell Lung Cancer

Inclusion Criteria: * Histologic or cytologic diagnosis of stage III non-small cell lung cancer; patients will need to meet the following criteria for stage IIIA or IIIB diagnosis: * IIIA * Histologic or cytologic diagnosis of ipsilateral mediastinal lymph node involvement, or * Tumors greater than 7 cm or with chest wall invasion, or involvement of one of the following diaphragm, phrenic nerve, mediastinal pleura or parietal pericardium with hilar or mediastinal lymph node involvement * More than one mediastinal lymph node enlarged on computed tomography (CT) scan and the same lymph nodes positive on positron emission tomography (PET) scans or * Paralyzed left vocal cord with separate lung primary distinct from the aorto-pulmonary lymph nodes on the CT scan * IIIB * Histologic or cytologic diagnosis of N3 lymph node involvement; or * Enlarged N3 lymph nodes on CT scan that are positive on PET scan as well; patient must not have extension of lymph node involvement to cervical lymph nodes other than supraclavicular lymph nodes; or * Right sided primary with left vocal cord paralysis; or * Evidence of tumor extension into the mediastinum and/or mediastinal structures either at the time of mediastinoscopy, bronchoscopy or on CT scans * Patients with a nodules in the same lung but no other areas of involvement * Patients with prior surgically resected stage I NSCLC who did not receive any adjuvant therapy, who now have stage IIIA or B NSCLC will be eligible * Southwestern Oncology Group (SWOG) performance status 0 or 1 * Absolute neutrophil count of \> 1.5 x 10\^9/L * Platelet count \> 100,000 x 10\^9/L * Serum creatinine =\< 1.5 times the institutional upper limit of normal (ULN) * Calculated creatinine clearance (Cockcroft-Gault formula) of \>= 45mL/min * Serum bilirubin \> ULN * Transaminases (serum glutamic oxaloacetic transaminase \[SGOT\] and/or serum glutamate pyruvate transaminase \[SGPT\]) \> 1.5 times institutional ULN * Alkaline phosphatase \>= 2.5 times ULN * Forced expiratory volume in one second (FEV1) of \>= 1 liter and diffusion capacity of carbon monoxide (DLCO) \>= 40% of predicted * Patient should undergo brain imaging (CT scan or magnetic resonance imaging \[MRI \]) to rule out brain metastases * Signed informed consent that details the investigational nature of the study according to institutional and federal guidelines * Registered with Clinical Trials Office at Karmanos Cancer Institute/Wayne State University Exclusion Criteria: * Prior chemotherapy, radiation for any malignancy in which they received any thoracic radiotherapy * Patients with concurrent malignancy; patients with prior or concurrent malignancy will be allowed as long as the treating physician considers it unlikely to impact the clinical outcome of the patient * Patients with peripheral neuropathy \> 2 * Serious medical illness including but not limited to uncontrolled congestive heart failure, uncontrolled angina, myocardial infarction or cerebrovascular event with 6 months of registration, history of chronic active hepatitis or history of human immunodeficiency virus (HIV) or an active bacterial infection will not be eligible * Inability or unwillingness to take folic acid or vitamin B12 or dexamethasone * Pregnant or lactating women; all pre-menopausal and peri-menopausal women should have a urine test for pregnancy within a week of starting therapy; all patients of child bearing potential should agree to use an effective contraceptive method * Patients should not participate in any other therapeutic investigational study while taking part in this study * Patients on warfarin will not be allowed on the study; patient on low molecular heparin or anti direct factor Xa inhibitor (Xa) drugs will be allowed * Patients with a soy allergy will be excluded