Local Ablative Therapy for Treatment of Oligoprogressive, EGFR-Mutated, Non-Small Cell Lung Cancer After Treatment With Osimertinib

* INCLUSION CRITERIA: For inclusion in the study subjects should fulfill the following criteria: * Provision of informed consent prior to any study specific procedures * Patients (male/female) must be greater than or equal to 18 years of age. * Patients with histologically confirmed, by the National Cancer Institute (NCI) Laboratory of Pathology or by Clinical Laboratory Improvement Amendments of 1988 (CLIA)-certified Next Generation Sequencing or Cobas estimated Epidermal Growth Factor Receptor (EGFR) Mutation Test v1/2 at an outside institution, advanced lung adenocarcinoma with EGFR-sensitizing somatic mutations or a germline T790M mutation (detected histologically or via circulating tumor deoxyribonucleic acid (ctDNA) analysis using a CLIA assay) with: * No prior EGFR tyrosine kinase inhibitor (TKI) therapy (Cohort 1) OR \-- Progressive disease after 1st or 2nd generation EGFR TKI therapy harboring somatic T790M mutation (Cohort 2) OR * Progressive disease after treatment with osimertinib who are eligible for local ablative therapy (Cohort 3) * Presence of measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1. * In patients with suspected leptomeningeal disease, the diagnosis of leptomeningeal disease should be confirmed by the presence of neurological or imaging signs and/or positive cerebrospinal fluid (CSF) cytology. * Eastern Cooperative Oncology Group (ECOG) performance status 0-2. * No uncontrolled arrhythmia; no myocardial infarction in the last 6 months. * Females should not be breast feeding and must have a negative pregnancy test prior to start of dosing if of child-bearing potential 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 old would be consider postmenopausal if they have been amenorrheic for 12 months or more following cessation of exogenous hormonal treatments and with luteinizing Hormone (LH) and follicle stimulating hormone (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 * Females of child-bearing potential should use reliable methods of contraception from the time of screening until 3 months after discontinuing osimertinib. Acceptable methods of contraception include total and true sexual abstinence, tubal ligation, hormonal contraceptives that are not prone to drug-drug interactions (IUS Levonorgestrel Intra Uterine System (Mirena), Medroxyprogesterone injections (Depo-Provera), copper-banded intra-uterine devices, and vasectomized partner. All hormonal methods of contraception should be used in combination with the use of a condom by their male sexual partner for intercourse. * Male patients should be willing to use barrier contraception. Male patients should be asked to use barrier contraceptives (i.e., by use of condoms) during sex with all of their female partners during the trial and for a washout period of 3 months. Patients should refrain from donating sperm from the start of dosing until 6 months after discontinuing osimertinib treatment. If male patients wish to father children, they should be advised to arrange for freezing of sperm samples prior to the start of osimertinib treatment. * Patient is willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations including follow up. EXCLUSION CRITERIA: Subjects should not enter the study if any of the following exclusion criteria are fulfilled: * Any unresolved toxicities from prior therapy greater than Common Terminology Criteria for Adverse Events (CTCAE) grade 1 at the time of starting study treatment with the exception, of alopecia and grade 2, prior platinum-therapy related neuropathy. * Treatment with an investigational drug within five half-lives of the compound. * Major thoracic or abdominal surgery from which the patient has not sufficiently recovered yet. * Untreated and uncontrolled second tumor in the past 2 years. * Patients currently receiving (or unable to stop use prior to receiving the first dose of study treatment) medications or herbal supplements known to be potent inhibitors of CYP3A4 (at least 1 week prior) and potent inducers of cytochrome P450 3A4 (CYP3A4) (at least 3 weeks prior) will only be eligible at the PI's discretion. * Any evidence of severe or uncontrolled systemic diseases, including uncontrolled hypertension and 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. Screening for chronic conditions is not required. * Patients with central nervous system (CNS) metastases who are neurologically unstable. * Past medical history of interstitial lung disease (ILD), drug induced ILD, radiation pneumonitis requiring steroid treatment, or any evidence of clinically active ILD * Inadequate bone marrow reserve or organ function as demonstrated by any of the following laboratory values: * Absolute neutrophil count \<1 x 10(9)/L * Platelet count \<100 x 10(9)/L * Hemoglobin \<90 g/L * Alanine aminotransferase \>2.5 times the 2.1.2.9.4 upper limit of normal (ULN) if no demonstrable liver metastases or \>5 times ULN in the presence of liver metastases * Aspartate aminotransferase \>2.5 times ULN if no demonstrable liver metastases or \>5 times ULN in the presence of liver metastases * Total bilirubin \>1.5 times ULN if no liver metastases or \>3 times ULN in the presence of documented Gilbert's Syndrome (unconjugated hyperbilirubinemia) or liver metastases * Creatinine \>1.5 times ULN concurrent with creatinine clearance \<30 ml/min (measured or calculated by Cockcroft and Gault equation); confirmation of creatinine clearance is only required when creatinine is \>1.5 times ULN * Any of the following cardiac criteria * Resting corrected QT interval (corrected QT interval (QTc) using Fredericia's formula) \> 480 msec * Any clinically important abnormalities in rhythm, conduction or morphology of resting electrocardiogram (ECG) (e.g., complete left bundle branch block, third degree heart block, second degree heart block) * 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 prolong the QT interval * Significant symptomatic congestive heart failure, per principal investigator (PI) judgement. * Refractory nausea and vomiting, chronic gastrointestinal diseases, inability to swallow the formulated product or previous significant bowel resection that would preclude adequate absorption of osimertinib * History of hypersensitivity to osimertinib (or drugs with a similar chemical structure or class to osimertinib) or any excipients of these agents * Judgment by the Investigator that the patient should not participate in the study if the patient is unlikely to comply with study procedures, restrictions, and requirements