Safety and Efficacy of Combination Osimertinib and Ipilimumab in Patients w EGFR Mutated NSCLC

Inclusion Criteria: * Male or female subject aged ≥ 18 years. * Histologically or cytologically confirmed metastatic, non-small cell lung cancer (NSCLC). * The presence of any sensitizing epidermal growth factor receptor (EGFR) tumor mutation. * Currently on a stable dose of osimertinib (40 mg or 80 mg daily) ≥ 28 days without clinical disease progression. * Eastern Cooperative Oncology Group (ECOG) Performance Status ≤ 2. * Adequate organ function as defined as: * Hematologic: * White blood cell count \> 2.0 k/microliter (uL) * Platelet count \> 75,000/mm3 * Hemoglobin ≥ 9 g/dL * Absolute neutrophil count (ANC) ≥ 1,000/mm3 * Hepatic: * Total Bilirubin ≤ 1.5 x institutional upper limit of normal (ULN) ---Except for patient with Gilbert's syndrome. * Aspartate aminotransferase (AST)(SGOT)/Alanine aminotransferase (ALT)(SGPT) ≤ 2.5 × institutional ULN * Renal: * eGFR ≥ 30 mL/min/1.73m2 or creatinine clearance ≥ 30 mL/min by Cockcroft-Gault: * Males: ((140-age)×weight\[kg\])/(serum creatinine \[mg/dL\]×72) * Females: (((140-age)×weight\[kg\])/(serum creatinine \[mg/dL\]×72))×0.85 * Concurrent enrollment in the study, "Rethinking Measurement of Performance Status in Cancer Patients," Institutional Review Board (IRB) # 112529. * Evidence of post-menopausal status or negative urinary or serum pregnancy test for female pre-menopausal patients. Women will be considered post-menopausal if they have been amenorrheic for 12 months without an alternative medical cause. The following age-specific requirements apply: * Women \<50 years of age would be considered post-menopausal if they have been amenorrheic for 12 months or more following cessation of exogenous hormonal treatments and if they have luteinizing hormone and follicle-stimulating hormone levels in the post-menopausal range for the institution or underwent surgical sterilization (bilateral oophorectomy or hysterectomy). * Women ≥50 years of age would be considered post-menopausal if they have been amenorrheic for 12 months or more following cessation of all exogenous hormonal treatments, had radiation-induced menopause with last menses \>1 year ago, had chemotherapy-induced menopause with last menses \>1 year ago, or underwent surgical sterilization (bilateral oophorectomy, bilateral salpingectomy or hysterectomy). * Highly effective contraception for both male and female subjects throughout the study and for at least 5 months after the last dose of study therapy for females and 7 months after the last dose for males if the risk of conception exists. * Recovery to baseline or ≤ Grade 1 CTCAE v.5 from toxicities related to any prior treatments, unless AE(s) are clinically non-significant and/or stable on supportive therapy. * Able to provide informed consent and willing to sign an approved consent form that conforms to federal and institutional guidelines. Exclusion Criteria: * Prior EGFR targeted therapy. * Prior radiation therapy within 2 weeks prior to cycle one day one. * Active or prior autoimmune disease that might deteriorate when receiving an immunostimulatory agent. Patients with diabetes type I, vitiligo, psoriasis, or hypo-or hyperthyroid disease not requiring immunosuppressive treatment are eligible. * Known history of: * Immune-mediated colitis, inflammatory bowel disease, or interstitial lung disease/pneumonitis. * Intra-abdominal abscess, GI obstruction and abdominal carcinomatosis which are known risk factors for bowel perforation. * Current use of immunosuppressive medication at the time of study enrollment, EXCEPT for the following permitted steroids: * Intranasal, inhaled, topical steroids, eye drops or local steroid injection (eg,intra-articular injection); * Systemic corticosteroids at physiologic doses ≤ 10mg/day of prednisone or equivalent; * Steroids as premedication for hypersensitivity reactions (e.g., computed tomography (CT) scan premedication). * Diagnosis of any other malignancy within 2 years prior to study enrollment, except for adequately treated basal cell or squamous cell skin cancer, carcinoma in situ of the breast, bladder or of the cervix, and low-grade (Gleason 6 or below) prostate cancer on surveillance with no plans for treatment intervention (e.g., surgery, radiation, or castration) or prostate cancer that has been adequately treated with prostatectomy or radiotherapy and currently with no evidence of disease or symptoms is allowed. * Uncontrolled central nervous system (CNS) metastases are not allowed; subjects with previously treated brain metastases will be allowed if the brain metastases have been treated, toxicities have resolved to grade 1 or baseline and steroids are no longer required. Leptomeningeal metastases are not allowed. * Patients with asymptomatic brain metastasis are allowed if previous steroid treatment was discontinued ≥ 6 weeks. * Patients with stable brain metastases on osimertinib therapy are eligible. * Palliative radiation therapy is allowed while on study therapy (see Section 6.4). * The subject has uncontrolled, significant intercurrent or recent illness including, but not limited to, the following conditions: * Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better. * Myocardial infarction, severe angina, or unstable angina within 6 months prior to administration of first dose of study drug. * Uncontrolled symptomatic hypertension that cannot be controlled with anti-hypertensive agents. * History of serious ventricular arrhythmia (i.e., ventricular tachycardia or ventricular fibrillation). * Cardiac arrhythmias requiring anti-arrhythmic medications (except for atrial fibrillation that is well controlled with anti-arrhythmic medication). * Coronary or peripheral artery bypass graft within 6 months of screening. * Corrected QT interval (QTc) prolongation \> 500 msec. * Active, clinically symptomatic left ventricular failure (left ventricle ejection fraction (LVEF) \< 50%). * Other clinically significant disorders that would preclude safe study participation. * Known HIV infection with a detectable viral load within 6 months of the anticipated start of treatment. -Note: Patients on effective anti-retroviral therapy with an undetectable viral load within 6 months of the anticipated start of treatment are eligible for this trial. * Known chronic hepatitis B virus (HBV) or hepatitis C virus (HCV) infection with a detectable viral load. -Note: Patients with an undetectable HBV viral load on appropriate suppressive therapy are eligible. Patients with an undetectable HCV viral load on appropriate treatment are eligible. * Vaccination with a live attenuated vaccine within 4 weeks of cycle one day one and while on trials is prohibited except for administration of inactivated vaccines. * Known prior severe hypersensitivity to investigational product or any component in its formulations, including known severe hypersensitivity reactions to monoclonal antibodies (NCI CTCAE v5.0 Grade ≥ 3). * Subjects taking prohibited medications as described in Section 6.4.2. A washout period of prohibited medications for a period of at least 5 half-lives or as clinically indicated should occur prior to the start of treatment. * Subject is a prisoner or involuntarily incarcerated or is compulsorily detained for treatment of either a psychiatric or physical illness (e.g. infectious disease).