A Phase 2 Study of Osimertinib in Combination With Selumetinib in EGFR Inhibitor naïve Advanced EGFR Mutant Lung Cancer

Inclusion Criteria: * Participants must have histologically confirmed stage IV NSCLC (per AJCC 7th edition) with either the L858R or exon 19 deletion activating EGFR mutation as identified in a CLIA-approved laboratory. --Note: recurrent stage IV disease initially diagnosed at an earlier stage is considered eligible, provided prior treatment criteria is met (see 3.1.3 and 3.2.1). * Participants must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as ≥20 mm with conventional techniques or as ≥10 mm with spiral CT scan, MRI, or calipers by clinical exam. * Participants can have no prior history of any EGFR-directed therapy, including TKIs or antibodies, and must also be chemotherapy and immunotherapy naïve for metastatic disease. Patients who have completed adjuvant or neo-adjuvant chemotherapy \> 6 months ago are considered treatment naïve * Participants must be aged ≥ 18 years * Participants must have an ECOG performance status of 0-1 (Appendix A) * Participants must have normal organ and marrow function as defined below: * absolute neutrophil count ≥1,500/mcL * platelets ≥100,000/mcL * hemoglobin \>9.0 g/dL * total bilirubin \< 1.5 times the ULN if no liver metastases or \< 3 times the ULN in the presence of documented Gilbert's syndrome (unconjugated hyperbilirubinemia) or liver metastases * AST(SGOT)/ALT(SGPT) \<2.5 × institutional upper limit of normal or \<5 times the ULN in the presence of liver metastases * creatinine ≤ 1.5 x institutional upper limit of normal OR * creatinine clearance ≥50 mL/min as determined by the Cockcrft-Gault formula. * Participants should have biopsy tissue (or a cell block from a malignant effusion) at time of diagnosis available for targeted next-generation sequencing. The testing does not have to be completed prior to study enrollment. Biopsy can be performed at an outside institution as long as sufficient tissue is available. --Note: if next generation sequencing has already been performed prior to study enrollment, it does not need to be repeated. Tissue is still requested for central NGS. * Participants must be ≥2 weeks since any major surgery (excluding vascular access placement, mediastinoscopy, or biopsies performed by an interventional service) * Participants must be ≥2 weeks since any prior radiation, including CNS radiation * Male patients: Willing to use adequate contraception (barrier or abstinence) while on treatment with study drug and for 3 months after finishing treatment. * Female patients: Willing to use adequate contraception (barrier or abstinence) at least 2 weeks before receiving any study medication, while on treatment with study drug, and for 3 months after finishing treatment. * Female patients: Must not be pregnant or breast-feeding. Women of child-bearing potential must have a negative pregnancy test prior to start of dosing or must have evidence of non-child-bearing potential by fulfilling one of the following criteria at screening: * Post-menopausal defined as aged more than 50 years and amenorrheic for at least 12 months following cessation of all exogenous hormonal treatments * Women under 50 years are considered postmenopausal if they have been amenorrheic for 12 months or more following cessation of exogenous hormonal treatments and with LH and FSH levels in the post-menopausal range for the institution. * Documentation of irreversible surgical sterilization by hysterectomy, bilateral oophorectomy, or bilateral salpingectomy but not tubal ligation Exclusion Criteria: * Prior or ongoing treatment with any of the following: * EGFR targeted therapy (TKI or antibody) or any other targeted therapies targeting the ERBB family * Any cytotoxic chemotherapy, investigational agents, or anticancer drugs for the treatment of advanced NSCLC * Prior radiotherapy \</= 2 weeks of the first dose of study treatment. * Uncontrolled central nervous system (CNS) disease, including parenchymal brain metastases, leptomeningeal disease, or spinal cord compression. Patients with asymptomatic untreated brain metastases are eligible. Patients with treated CNS disease will be allowed to enroll provided they have clinically confirmed stable disease with ≥2 weeks since definitive CNS therapy (radiation or surgery) and ≥2 weeks without systemic steroids. Patients may undergo either whole brain radiation or stereotactic radiosurgery prior to study entry. * History of allergic reactions attributed to compounds, or any of its excipients, of similar chemical or biologic composition to osimertinib or selumetinib. * Patients currently receiving and unable to stop using medications known to be potent inhibitors or inducers of CYP3A4. The full list of medications that would make a patient ineligible are provided in Appendix B, along with indicated washout times. * Patients currently receiving and unable to stop high doses of supplemental vitamin E. Selumetinib capsules contain vitamin E and high doses of vitamin E have been reported to cause bleeding and interfere with blood coagulation processes. * Any unresolved toxicities from prior therapy greater than Common Terminology Criteria for Adverse Events (CTCAE) grade 1 at the time of starting study treatment. * Malignancies within the past 3 years excluding adequately treated basal or squamous cell carcinomas of the skin without local or distant metastases and cancer of the cervix in situ. * Refractory nausea and vomiting, chronic gastrointestinal diseases, previous significant bowel resection, or any process that compromises the ability to swallow or absorb oral medication * Significant medical history or unstable medical comorbidities, including: * heart disease including congestive heart failure (NYHA Grade II or greater); unstable angina; prior myocardial infarction (NSTEMI or STEMI) within 6 months prior to study enrollment; hypertension with a systolic blood pressure of \>150 mm Hg or diastolic blood pressure of \>100 mm Hg while on antihypertensive medication; previous moderate or severe impairment of left ventricular systolic function (LVEF \<45% on echocardiography or equivalent on MUGA) even if full recovery has occurred; prior or current severe valvular heart disease; prior or current cardiomyopathy including but not limited to the following: * Known hypertrophic cardiomyopathy * Known arrhythmogenic right ventricular cardiomyopathy * any clinically important abnormalities in rhythm, conduction or morphology of resting ECG, e.g. complete left bundle branch block, third-degree heart block, second-degree heart block, QT interval corrected by Fridericia's formula (QTcF) of \>/= 450 ms in males or \>/= 450 ms in females. Formula: QTc=QT/(RR\^1/3) * any factors that increase the risk of QTc prolongation or risk of arrhythmic events such as heart failure, hypokalemia, congenital long QT syndrome, family history of long QT syndrome or unexplained sudden death under 40 years of age in first degree relatives, or any concomitant medication known to the prolong the QT interval and listed in Appendix B that a patient is unable to stop. * past medical history of interstitial lung disease, drug-induced interstitial lung disease, radiation pneumonitis which required steroid treatment, or any evidence of clinically active interstitial lung disease * active bleeding diatheses, which in the investigator's opinion makes it undesirable for the patient to participate in the trial or which would jeopardize compliance with the protocol * active infection or ongoing antiviral medication for viral infections including hepatitis B, hepatitis C, or human immunodeficiency virus (HIV). Screening for chronic conditions is not required. HIV-positive participants on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with selumetinib or osimertinib. * Baseline left ventricular ejection fraction (LVEF) below the LLN or of \< 45% measured by echocardiography/MUGA; atrial fibrillation with a ventricular rate \> 100 bpm on ECG at rest. * Any evidence of severe or uncontrolled systemic diseases, including active bleeding diatheses, which in the investigator's opinion makes it undesirable for the patient to participate in the trial or which would jeopardize compliance with the protocol * Known to be T790M+ (on pre-treatment tumor or plasma) or known germline T790M. * Ophthalmological conditions as follows: * Current or past history of retinal pigment epithelial detachment (RPED)/central serous retinopathy (CSR) or retinal vein occlusion * Uncontrolled glaucoma (irrespective of IOP) * Males and females of reproductive potential who are not using an effective method of birth control and females who are pregnant or breastfeeding or have a positive (urine or serum) pregnancy test prior to study entry. * Pregnant women are excluded from this study because the effects of selumetinib and osimertinib on the development of the fetus are unknown, and there is potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with selumetinib or osimertinib, breastfeeding should be discontinued if the mother is treated with these agents.