A Phase 2 Randomized Study of Osimertinib Versus Osimertinib Plus Chemotherapy for Patients With Metastatic EGFR-Mutant Lung Cancers That Have Detectable EGFR-Mutant cfDNA in Plasma After Initiation of Osimertinib

Inclusion Criteria: Inital * Age ≥ 18 years * Biopsy proven metastatic non-small cell lung cancer, confirmed at enrolling institution * Somatic activating mutation in EGFR in pre-treatment tumor biopsy/ cytology from pleural fluid or cfDNA * Either have not started a prior EGFR TKI therapy or may have started osimertinib within 3 weeks of confirming eligibility and enrollment criteria of measurable disease per approval of PI, with no prior chemotherapy for treatment of metastatic disease (adjuvant therapy \> 6 months prior to study start is acceptable) * Measurable (RECIST 1.1) indicator lesion not previously irradiated with measurable disease determined per treating investigator. If a patient has already started on osimertinib there must be available pre-osimertinib baseline tumor assessments , or tumor assessments within +7 days of Osimertinib start, to be utilized for RECIST 1.1 assessment. * Karnofsky performance status (KPS)≥70%, * Ability to swallow oral medications * Adequate organ function (use of G-CSF and/or transfusion to meet these criteria are not allowed) * Hemoglobin ≥ 9 g/dL * Platelets ≥ 150,000mm\^3 or 150 x 10\^9/L * AST, ALT ≤ 2.5 x ULN with no liver metastases or \< 5x ULN with the presence of liver metastases * Total bilirubin ≤ 1.5 x ULN if no liver metastases or \< 3 x ULN in the presence of documented Gilbert's Syndrome (unconjugated hyperbilirubinemia) or liver metastases * Absolute neutrophil count (ANC) ≥ 1500 cells/mm\^3 * Creatinine ≤ ULN OR calculated creatinine clearance ≥ 60ml/min calculated by Cockcroft and Gault equation * Creatinine clearance ≥ 60 mL/min calculated by Cockcroft and Gault equation * Willing to use highly effective contraceptive measures if of child-bearing potential or if the patient's sexual partner is a woman of child-bearing potential: * Female subjects should be using highly effective contraceptive measures, and must have a negative pregnancy test and not be breast-feeding prior to start of dosing through 6 weeks after discontinuing the study drug 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 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 * Male subjects should be willing to use barrier contraception and avoid sperm donation prior to the start of dosing through 4 months of discontinuing the study drug Exclusion Criteria: Initial * Pregnant or lactating women * Any radiotherapy within 1 week prior to starting treatment on protocol. The washout window only applies for patients who have not started Osimertinib. * Any major surgery within 2 weeks of starting treatment on protocol. The washout window only applies for patients who have not started Osimertinib. * Any evidence of clinically significant interstitial lung disease * Treatment with an investigational drug within five half-lives of the compound or 3 months, whichever is greater * Currently receiving (or unable to stop prior to receiving the first dose of study treatment) medications or herbal supplements known to be strong inducers of CYP3A4. All patients must try to avoid concomitant use of any medications, herbal supplements and/or ingestion of foods with known inducer effects on CYP3A4. * Any unresolved toxicities from prior therapy greater than CTCAE grade 1 at the time of starting study treatment, with the exception of alopecia and grade 2 prior platinum-therapy- related neuropathy * 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 * active infection including hepatitis B, hepatitis C and human immunodeficiency virus (HIV). Screening for chronic conditions is not required. * Screening for chronic conditions is not required. * In patients with resolved or chronic hepatitis B infection (inactive carrier state) or active controlled HBV infection on treatment with osimertinib * Recommend monthly monitoring of ALT/AST, HBV DNA levels and HBsAg (if negative at baseline) * Where liver signs and symptoms of viral reactivation appear (HBV DNA levels exceeding 10-fold from baseline or ≥100 IU/ml (if baseline HBV DNA levels are undetectable) or conversion of HBsAg negative to positive): * Expert hepatologist/specialist oversight of the patient is required * Consider interruption or discontinuation of study treatment, based on riskbenefit assessment * Refractory nausea and vomiting, chronic gastrointestinal diseases, inability to swallow the tablets or previous significant bowel resection that would preclude adequate absorption of osimertinib. * Any of the following cardiac criteria: * Mean resting corrected QT interval (QTc) \> 470 msec where QT interval is corrected for heart rate using Frederica's formula (QTcF). * Any clinically important abnormalities in rhythm, conduction or morphology of resting ECG e.g. complete left bundle branch block, third degree heart block and second degree heart block. * Patient with any factors that increase the risk of QTc prolongation or risk of arrhythmic events such as heart failure, electrolyte abnormalities (including: Serum/Plasma potassium \<LLN, Serum/Plasma Magnesium \<LLN; Serum/Plasma Calcium \<LLN), 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 and cause Torsades de Pointes.If concomitant medication can not be discontinued, please notify and confirm with MSK PI prior to enrollment. * 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. * History of hypersensitivity to active or inactive excipients of osimertinib or drugs with a similar chemical structure or class to osimertinib. * 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. Inclusion Criteria: Randomization * Patients with detectable plasma EGFR mutations at C2D1 * Karnofsky performance status (KPS) ≥ 70% * Adequate organ function * Hemoglobin ≥ 9 g/dL * Platelets ≥ 100,000mm\^3 or 100 x 10\^9/L * Creatinine ≤ ULN OR calculated creatinine clearance ≥ 60ml/min * AST, ALT ≤ 3x ULN with no liver metastases or ≤ 5x ULN with the presence of liver metastases * Total bilirubin ≤ 1.5 x ULN if no liver metastases or ≤ 3 x ULN in the presence of documented Gilbert's Syndrome (unconjugated hyperbilirubinemia) or liver metastases * Absolute neutrophil count (ANC) ≥ 1500 cells/mm3Must have at least stable disease per RECIST 1.1 assessment prior to initiating chemotherapy at C4D1 * Eligibility testing (KPS, bloodwork) should be tested at C3D1. If the subject's evaluation does not meet eligibility criteria, any result obtained between C3 and C4 can be used Please note: All 'Initial' Exclusion Criteria must be re-confirmed prior to randomization, except for the cardiac criteria related to the ECG. The ECG does not need to be repeated for patients screening for Randomization.