A Study of EGF816 and Gefitinib in TKI-naïve EGFR-mutant Non-Small Cell Lung Cancer

Inclusion Criteria: * Participants must have a pathologically-confirmed diagnosis of non-small cell lung cancer (NSCLC). * Participants must have advanced disease - either stage IV disease, stage IIIB disease not amenable to definitive multi-modality therapy, or recurrent disease after a prior diagnosis of stage I-III disease. All staging is via the American Joint Committee on Cancer (AJCC)/IASLC 7th edition proposed staging criteria * An EGFR sensitizing mutation must be detected in tumor tissue. Specifically, patients harboring the most common mutations, deletions in exon 19 or the L858R mutation in exon 21 are eligible. Other EGFR sensitizing mutations may be eligible after discussion with the principal investigator. Patients may be enrolled in the study based on an activating EGFR mutation detected by a CLIA-certified tissue or plasma-based assay, but will be required to undergo a mandatory tumor biopsy during study screening. * Participants must have measurable disease, per RECIST 1.1. See Section 11 for the evaluation of measurable disease. * Patients in the six patient safety run-in cohort may have had a prior EGFR TKI in the metastatic setting (to allow for patients who started initial therapy at an outside hospital), but treatment duration must have been less than three months. After the initial six-patient safety run-in, no prior EGFR TKI therapy in the metastatic setting is allowed. An EGFR TKI given in the adjuvant setting (i.e. with no measurable disease at the time of administration) is allowable provided the subject has been off of EGFR TKI therapy for at least six months at the time of enrollment. * Patients may have had no more than one prior line of chemotherapy or immunotherapy in the metastatic setting. At least 14 days must have elapsed from the last chemo/immunotherapy administration until the start of protocol treatment, and patients must have recovered from the side effects of any of these agents. * Patients must be screened for HBV. Patients who are either HBsAg positive or HBV-DNA positive must be willing and able to take antiviral therapy 1-2 weeks prior to 1st dose of study treatment and continue on antiviral therapy for at least 4 weeks after the last dose of EGF816. Additional management of the patients would be provided by a physician with expertise in management of HBV, if needed. Patients must have negative hepatitis C antibody (HCV-Ab) or positive HCV-Ab but undetectable level of HCV-RNA. Note: patients with detectable HCV-RNA are not eligible for the study. * Patients must receive insurance approval for or be willing to pay for commercial gefitinib. * Age \>/= 18 years. * ECOG performance status ≤2 (Karnofsky ≥60%, see Appendix A) * Life expectancy of greater than 12 weeks. * Participants must have normal organ and marrow function as defined below: * Leukocytes ≥3,000/mcL * Absolute neutrophil count ≥1,500/mcL * Platelets ≥100,000/mcL * Total bilirubin \>1.5 x upper limit of normal (ULN) \*For patients with Gilbert's syndrome total bilirubin \>3.0 x ULN * AST(SGOT)/ALT(SGPT) ≤3 × institutional upper limit of normal; for patients with known hepatic metastases AST and/or ALT \> 5x ULN * Creatinine ≤1.5 × institutional upper limit of normal * The effects of EGF816 and gefitinib on the developing human fetus are unknown. For this reason, women of child-bearing potential and men must agree to use highly effective contraception during the study and for 3 months after stopping the study treatment. Highly effective contraception methods include: * Total abstinence (when this is in line with the preferred and usual lifestyle of the subject. Periodic abstinence (e.g., calendar, ovulation, symptom thermal, postovulation methods) and withdrawal are not acceptable methods of contraception * Female sterilization (have had surgical bilateral oophorectomy with or without hysterectomy) or tubal ligation at least six weeks before taking study treatment. In case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment * Male Partner: male sterilization (at least 6 months prior to screening). For female subjects on the study the vasectomized male partner should be the sole partner for that subject. * Combination of any two of the following (a+b or a+c, or b+c): * A. Use of oral, injected or implanted hormonal methods of contraception or other forms of hormonal contraception that have comparable efficacy (failure rate \<1%), for example hormone vaginal ring or transdermal hormone contraception. * B. Placement of an intrauterine device (IUD) or intrauterine system (IUS) * C. Barrier methods of contraception: Condom or Occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/vaginal suppository. * D. In case of use of oral contraception women should have been stable on the same pill for a minimum of 30 days before taking study treatment. * Women are considered post-menopausal and not of childbearing potential if they have had 12 months of natural (spontaneous) amenorrhea with an appropriate clinical profile (e.g. age appropriate, history of vasomotor symptoms) or have had surgical bilateral oophorectomy (with or without hysterectomy) or tubal ligation at least six weeks ago. In the case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment is she considered not of childbearing potential. * Sexually active males must agree to use a condom during intercourse while taking drug and for 3 months after stopping treatment; men should not father a child in this period. A condom is required to be used also by vasectomized men in order to prevent delivery of the drug via seminal fluid. * Ability to understand and the willingness to sign a written informed consent document. Written informed consent must be obtained prior to any screening procedures. Exclusion Criteria: * Participants with clinically active or symptomatic interstitial lung disease or interstitial pneumonitis (i.e., affecting activities of daily living or requiring therapeutic intervention) and patients with history of clinically significant interstitial lung disease or radiation pneumonitis. * Patients with clinically symptomatic brain metastases or leptomeningeal disease. Patients may be on a stable dose of corticosteroids to control brain metastases if they have been on a stable dose for two weeks prior to study treatment and are clinically asymptomatic. * Patients who have had radiation to the lung fields within four weeks of starting treatment. For patients receiving palliative radiation to thoracic vertebrae, ribs or other sites where the radiation field includes the lungs, radiation must be completed at least two weeks before starting treatment. For all palliative radiation to all other sites, at least 7 days must have elapsed prior to starting to treatment. At least six months must have elapsed from radiation given with curative intent. * Patients who have had major surgery (e.g., intra-thoracic, intra-abdominal or intra-pelvic) within 2 weeks prior to starting study drug or who have not recovered from side effects of such procedure. Video-assisted thoracic surgery (VATS) and mediastinoscopy will not be counted as major surgery and patients can be enrolled in the study ≥1 week after the procedure. * Patients unable or unwilling to undergo a biopsy for research during the screening period, 2-3 weeks into the course of therapy and at the time of progression. * Patients with a second, clinically active, cancer. Patients with second cancers which have been treated with curative intent and/or are currently inactive are allowed. * Patients who have undergone a bone marrow or solid organ transplant. * Known history of human immunodeficiency virus (HIV) seropositivity (HIV testing is not mandatory). * Participants who are receiving any other investigational agents. Patients previously treated with investigational agents must complete a washout period of at least one week or five half-lives, whichever is longer, before starting treatment. * Patients receiving concomitant immunosuppressive agents or chronic corticosteroid use, except those on steroid to control brain metastases, those on topical or inhaled steroids, or steroids given via local injection. * Patients with clinically significant, uncontrolled cardiovascular disease, such as: * Unstable angina within 6 months prior to screening * Myocardial infarction within 6 months prior to screening * Patients with a history of documented congestive heart failure (New York Heart Association functional classification III-IV) * Peripheral vascular disease * Patients with uncontrolled hypertension defined as a Systolic Blood Pressure (SBP) ≥ 160 mm Hg and/or Diastolic Blood Pressure (DBP) ≥ 100 mm Hg, with or without anti-hypertensive medication. Initiation or adjustment of antihypertensive medication(s) is allowed prior to screening * Ventricular arrhythmias * Supraventricular and nodal arrhythmias not controlled with medication * Other cardiac arrhythmia not controlled with medication * Patients with corrected QT (QTc) ≥450 ms (male patients) or ≥460 ms (female patients) using Fridericia correction (QTcF) on the screening ECG (using triplicate ECGs) * Patients with history of congenital long QT syndrome or history of torsade de pointes * History of allergic reactions attributed to compounds of similar chemical or biologic composition to EGF816 or gefitinib. * Participants receiving any medications or substances that are strong inhibitors or inducers of CYP3A4 are ineligible. Because the lists of these agents are constantly changing, it is important to regularly consult a frequently-updated list such as http://medicine.iupui.edu/clinpharm/ddis/table.aspx; medical reference texts such as the Physicians' Desk Reference may also provide this information. As part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product. * Unable or unwilling to swallow tablets or capsules. * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study because the effects of EGF816 and gefitinib on a developing fetus are unknown. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with EGF816 or gefitinib, breastfeeding should be discontinued if the mother is treated with EGF816 and gefitinib