Personalized Adaptive Radiation Therapy With Individualized Systemic Targeted Therapy (PARTIST) for Locally Advanced, Non-small Cell Lung Cancer With Genomic Driver Mutations

Inclusion Criteria: * Patients with FDG-avid (radioactive glucose) and pathologically proven stage IIA-IIB or IIIA-IIIB non-small cell lung cancer (according to AJCC \[American Joint Committee on Cancer\] staging, 7th edition). * Patients with tumors that harbor either EGFR sensitizing mutations or ALK rearrangement. * Patients must be considered unresectable or medically inoperable; patients who decline surgery are also eligible. * Patients must be 18 years of age or older. * Patients with ECOG (Eastern Cooperative Oncology Group) performance status of 0-2. * Patients must have adequate organ function. * Patients must be able to take oral medications. * Women with reproductive capability must be willing to use effective contraception. * Patients must be informed of the investigational nature of this study and sign written informed consent in accordance with institutional and federal guidelines. * Patients must be willing to comply with study procedures. Exclusion Criteria: * Patients with tumors that have a component of small cell carcinoma. * Patients wtih stage I, II, or IV disease, including malignant pleural or pericardial effusion. * Prior radiotherapy to the thorax such that composite radiation would significantly over-dose critical structures, either per estimation of the treating radiation oncologist or defined by failure to meet normal tissue tolerance constraints. * Patients who cannot tolerate thoracic radiotherapy or targeted therapy. * Patients wtih a prior diagnosis of interstitial lung disease or pulmonary fibrosis. * Patients who cannot take oral medication, require intravenous alimentation, had prior surgical procedures affecting gastrointestinal absorption, or have active peptic ulcer disease. * Hypersensitivity to erlotinib, crizotinib, or to any of the excipients. * Pregnant women are excluded from this study because radiation has the potential for teratogenic or abortifacient effects. * Prisoners are excluded from this study.