Study of Dacomitinib and Osimertinib for Patients With Advanced EGFR Mutant Lung Cancer

Inclusion Criteria: * Written informed consent * Advanced biopsy-proven metastatic non-small cell lung cancer * Somatic activating mutation in EGFR in a tumor biopsy * No prior EGFR inhibitor treatment (gefitinib, afatinib, erlotinib, dacomitinib, osimertinib) however, prior treatment with other chemotherapies are allowed * Archival tissue available from a pre-treatment tumor biopsy or willing to undergo a tumor biopsy prior to study initiation. * Measurable (RECIST 1.1) indicator lesion not previously irradiated * Karnofsky performance status (KPS) ≥ 70% * Age \>18 years old * Ability to swallow oral medication * Agree to use effective methods of contraception from the time of screening until 3 months after treatment discontinuation (for males and females of child-bearing potential) * Adequate organ function * AST, ALT ≤ 3 x ULN * Total bilirubin ≤1.5x ULN * Creatinine ≤ 1.5x ULN OR calculated creatinine clearance ≥ 60ml/min * Absolute neutrophil count (ANC) ≥ 1000 cells/mm\^3 * Hemoglobin≥9.0 g/dL * Platelets ≥100,000/mm\^3 Exclusion Criteria: * Pregnant or lactating women * Any radiotherapy within 1 week of starting treatment on protocol. * Any major surgery within 1 weeks of starting treatment on protocol. * Any evidence of active clinically significant interstitial lung disease * A mean QTc \>470ms (Fridericia"s correction), clinically important arrhythmia, conduction or morphology of resting ECG (eg complete LBBB, 1st -3rd degree heart block, any factors that increase the risk of QTc prolongation or risk of arrhythmia) * Cardiovascular disease or cerebrovascular disease, CVA or MI \< 6 months prior to study enrollment, unstable angina, NYHA \>Grade II CHF, or serious cardiac arrhythmia uncontrolled by medication or with the potential to interfere with protocol treatment * History of pneumonitis or interstitial lung disease (ILD), drug induced ILD, radiation pneumonitits that required steroid treatment, and any evidence of clinically active ILD * Serious chronic GI conditions associated with diarrhea * Symptomatic, unstable brain metastases requiring escalating doses of steroids * Continue to have unresolved \> CTCAE grade 1 toxicity from any previous treatment