Dasatinib and Osimertinib (AZD9291) in Advanced Non-Small Cell Lung Cancer With EGFR Mutations

Inclusion Criteria: * Patients must have cytologically or histologically confirmed advanced NSCLC. Patients with mixed histology containing a small cell lung cancer component are not eligible. * Patients must have adequate archival material from a previous biopsy to determine EGFR mutation status and Cripto-1 expression, or undergo a biopsy of fresh tissue of the primary cancer or a metastatic site in order to make these determinations, if archival material is not available. * Presence of sensitizing EGFR mutations (deletion in exon 19, L858R in exon 21, G719X, and L861Q). Patients with the T790M mutation will also be eligible. * No prior treatment with an EGFR TKI for the advanced NSCLC. * ECOG performance status of 0-2. * Patients must have measurable disease by RECIST criteria, defined as at least one lesion 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. See Section 7.1.2 for the evaluation of measurable disease. * Prior systemic treatment is allowed, but toxicities of prior therapy must be resolved to grade 1 or less as per Common Terminology Criteria for Adverse Events (CTCAE) version 4.03. * Adequate organ and bone marrow function (hemoglobin \> 9 g/dL; absolute neutrophil count \> 1.5 x 109/L; platelet counts \> 100 x 109/L; serum bilirubin \< 2 x ULN; alanine aminotransferase (ALT) and aspartate aminotransferase (AST) \< 2.5 x ULN or \< 5 x ULN if liver metastases; calculated creatinine clearance \> 50 mL/min). * No uncontrolled arrhythmia; no myocardial infarction in the last 6 months. * Life expectancy of at least 12 weeks. * Age \> 18 years. * Ability to understand and willingness to sign a written informed consent document. Exclusion Criteria: * Patients who have had radiotherapy (except for palliative reasons), immunotherapy or chemotherapy during the previous 4 weeks (6 weeks for nitrosoureas or mitomycin) before treatment, or those who have ongoing toxic manifestations of previous treatments, with the exception of alopecia, of grade higher than 1. * Major thoracic or abdominal surgery from which the patient has not sufficiently recovered yet. * Untreated and uncontrolled second tumor in the past 2 years. * Logistical or psychological hindrance to participation in clinical research. * Patients with untreated symptomatic brain metastases may be eligible if symptoms do not require urgent surgery or radiation, and no steroids are necessary. * Patients with evidence of interstitial lung disease (bilateral, diffuse, parenchymal lung disease). * Pleural or pericardial effusions of any grade at study entry. Subjects previously diagnosed with pleural/pericardial effusion of any grade resolved at the time of study entry are allowed. * Ability to become pregnant (or already pregnant or lactating). Women and men who want to participate have to agree to use two highly effective forms of contraceptive prior to study entry, for the duration of study participation, and for 30 days following completion of therapy, to be eligible. Women of childbearing potential (WOCBP) must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG) within 24 hours prior to the start of study drug. * At high medical risk because of non-malignant systemic disease including uncontrolled infection. * Known to be serologically positive for hepatitis B, hepatitis C or HIV. * Uncontrolled or significant cardiovascular disease, including any of the following: * QTc interval \> 480 msec (mean value and manually verified) at 3 or more time points within a 24 hour period if necessary. * Diagnosed or expected congenital long QT syndrome. * Concurrent congestive heart failure, prior history of class III/IV cardiac disease (New York Heart Association). * Left ventricular ejection fraction \< 50% * Prior history of cardiac ischemia or cardiac arrhythmia within the last 6 months. Coronary angioplasty or stenting in the previous 12 months. * Any history of second or third degree heart block (may be eligible if the subject currently has a pacemaker). * Uncontrolled hypertension defined as inability to maintain blood pressure below the limit of 140/90 mmHg. * Known pulmonary hypertension. * History of significant bleeding disorder unrelated to CML, including: * Diagnosed congenital bleeding disorders (e.g. von Willebrand's disease) * Diagnosed acquired bleeding disorder within one year (e.g. acquired anti-factor VII antibodies) * Any other medical condition that in the Investigator's opinion would not make the patient a good candidate for the study.