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.