Combination Chemotherapy, Radiation Therapy, and Gefitinib in Treating Patients With Stage III Non-Small Cell Lung Cancer

Inclusion Criteria: * Histologically or cytologically documented non-small cell lung cancer (NSCLC), including squamous cell carcinoma, adenocarcinoma (including bronchoalveolar cell), and large cell anaplastic carcinoma (including giant and clear cell carcinomas) * ELIGIBLE DISEASE STAGES: Inoperable IIIA and selected IIIB * Generally, patients entered must be considered unresectable or inoperable; patients with T1 or T2, N2 disease are eligible; patients with T3, N2 or T4, N0-N2 disease are eligible if based on the closeness to the carina, invasion of the mediastinum or invasion of the chest wall; patients with T3, N0-N1 disease are not eligible; patients must be M0 (M1 patients are not eligible) * Patients with direct invasion of vertebral body are ineligible * Patients with tumors adjacent to a vertebral body are eligible, unless there is demonstrable bone invasion, as long as all gross disease can be encompassed in the radiation boost field in accordance with the homogeneity criteria * Patients with contralateral mediastinal disease (N3) are eligible if all gross disease can be encompassed in the radiation boost field in accordance with the homogeneity criteria; patients with scalene, supraclavicular, or contralateral hilar node involvement are ineligible * Patients with a pleural effusion, which is a transudate, cytologically negative and non-bloody, are eligible if the radiation oncologist feels the tumor can be encompassed within a reasonable field of radiotherapy. Patients with exudative, bloody, or cytologically malignant effusions are not eligible; if a pleural effusion can be seen on the chest computed tomography (CT) but not on chest x-ray (CXR) and is too small to tap, the patient will be eligible; a pleural effusion appearing only after a thoracotomy or other invasive thoracic procedure was attempted will not make a patient ineligible * PATIENTS MUST HAVE MEASURABLE DISEASE * Lesions that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>= 20 mm with conventional techniques or as ≥10 mm with spiral CT scan * Lesions that are not considered measurable include the following: * Bone lesions * Leptomeningeal disease * Ascites * Pleural/pericardial effusion * Abdominal masses that are not confirmed and followed by imaging techniques * Cystic lesions * Tumor lesions situated in a previously irradiated area * PRIOR THERAPY * \>= 2 weeks since formal exploratory thoracotomy. * No prior chemotherapy or radiation therapy for NSCLC * CTC performance status 0-2 * No "currently active" second malignancy other than non-melanoma skin cancers; patients are not considered to have a "currently active" malignancy if they have completed therapy and are considered by their physician to be at less than 30% risk of relapse * Non-pregnant and non-nursing because of significant risk to the fetus/infant * No patients with 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 * No patients with chronic gastrointestinal disorders including liver disease, diarrheal or emetic disorders, or malabsorptive conditions which could worsen toxicity or limit efficacy of ZD1839 * No cytochrome P450 3A4 (CYP3A4) inducers within 7 days prior to starting protocol therapy and while on protocol treatment. CYP3A4 inducers: phenytoin, carbamazepine, barbiturates, rifampicin, dexamethasone, and St John's Wort; single doses of dexamethasone used as an antiemetic are permitted * No human immunodeficiency virus (HIV)-positive patients receiving combination anti-retroviral therapy * Granulocytes \>= 1,500/ul * Platelets \>= 100,000/ul * Calculated creatinine clearance \>= 20 cc/min * Bilirubin \< 1.5 mg/dl * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) \< 2 x upper limit of normal (ULN)