Erlotinib Hydrochloride or Crizotinib and Chemoradiation Therapy in Treating Patients With Stage III Non-small Cell Lung Cancer

Inclusion Criteria: * Histologically or cytologically confirmed, newly diagnosed non-squamous NSCLC * Unresectable stage IIIA or IIIB disease; patients must be surgically staged to confirm N2 or N3 disease; patients may have invasive mediastinal staging by mediastinoscopy, mediastinotomy, endobronchial ultrasound transbronchial aspiration (EBUS-TBNA), endoscopic ultrasound (EUS), or video-assisted thoracoscopic surgery (VATS) * Patients with any tumor (T) with node (N)2 or N3 are eligible; patients with T3, N1-N3 disease are eligible if deemed unresectable; patients with T4, any N are eligible * Patients must have measurable disease, i.e., lesions that can be accurately measured in at least 1 dimension (longest dimension in the plane of measurement is to be recorded) with a minimum size of 10 mm by computed tomography (CT) scan (CT scan slice thickness no greater than 5 mm) * 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 * If a pleural effusion can be seen on the chest CT but not on chest x-ray and is too small to tap, the patient will be eligible; patients who develop a new pleural effusion after thoracotomy or other invasive thoracic procedure will be eligible * The institution's pre-enrollment biomarker screening at a Clinical Laboratory Improvement Amendments (CLIA) certified lab documents presence of known "sensitive" mutations in epidermal growth factor receptor tyrosine kinase (EGFR TK) domain (exon 19 deletion, L858) and/or EML4-anaplastic lymphoma kinase (ALK) fusion arrangement; either the primary tumor or the metastatic lymph node tissue may be used for testing of mutations * The institution's pre-enrollment biomarker screening at a CLIA certified lab documents absence of T790M mutation in the EGFR TK domain * Appropriate stage for protocol entry, including no distant metastases, based upon the following minimum diagnostic workup: * History/physical examination, including recording of pulse, blood pressure (BP), weight, and body surface area, within 45 days prior to registration * Whole body fludeoxyglucose-positron emission tomography (FDG-PET)/CT (orbits to mid-thighs) within 30 days prior to registration; PET/CT must be negative for distant metastasis * CT scan with contrast of the chest and upper abdomen to include liver and adrenals (unless medically contraindicated) within 30 days prior to registration * Magnetic resonance imaging (MRI) of the brain with contrast (or CT scan with contrast, if MRI medically contraindicated) within 30 days prior to registration * Zubrod performance status 0-1 within 14 days prior to registration * Absolute neutrophil count (ANC) \>= 1,000 cells/mm\^3 * Platelets \>= 100,000 cells/mm\^3 * Hemoglobin \>= 8.0 g/dl (Note: the use of transfusion or other intervention to achieve hemoglobin \[Hgb\] \>= 8.0 g/dl is acceptable) * Serum creatinine \< 1.5 mg/dL or calculated creatinine clearance \>= 50 ml/min (by Cockcroft-Gault formula) within 14 days prior to registration * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 2.5 x upper limit of normal (ULN) within 14 days prior to registration * Bilirubin within normal institutional limits within 14 days prior to registration * Negative serum pregnancy test within 14 days prior to registration for women of childbearing potential * Patient must provide study specific informed consent prior to study entry, including consent for mandatory screening of tissue Exclusion Criteria: * Prior invasive malignancy (except non-melanomatous skin cancer) unless disease free for a minimum of 730 days (2 years) (for example, carcinoma in situ of the breast, oral cavity, or cervix are all permissible) * Prior systemic chemotherapy for the study cancer; note that prior chemotherapy for a different cancer is allowable * Prior radiotherapy to the region of the study cancer that would result in overlap of radiation therapy fields * Atelectasis of the entire lung * Contralateral hilar node involvement * Exudative, bloody, or cytologically malignant effusions * Severe, active co-morbidity, defined as follows: * Unstable angina and/or congestive heart failure requiring hospitalization within the last 6 months * Transmural myocardial infarction within the last 6 months * Acute bacterial or fungal infection requiring intravenous antibiotics at the time of registration * Chronic obstructive pulmonary disease exacerbation or other respiratory illness requiring hospitalization or precluding study therapy at the time of registration; hepatic insufficiency resulting in clinical jaundice and/or coagulation defects * Acquired immune deficiency syndrome (AIDS) based upon current Centers for Disease Control and Prevention (CDC) definition; note, however, that human immunodeficiency virus (HIV) testing is not required for entry into this protocol; protocol-specific requirements may also exclude immuno-compromised patients * Pregnancy or women of childbearing potential and men who are sexually active and not willing/able to use medically acceptable forms of contraception * Prior allergic reaction to the study drug(s) involved in this protocol