Osimertinib, Surgery, and Radiation Therapy in Treating Patients With Stage IIIB or IV Non-small Cell Lung Cancer With EGFR Mutations, NORTHSTAR Study

Inclusion Criteria: * Histologically or cytologically confirmed non-small cell lung cancer * Stage IIIB/IV or recurrent non-small cell lung cancer which is not amenable to curative intent therapy * Patients must have one of the following: * NSCLC which harbors EGFR exon 19 deletion or L858R mutation. This subset of patients must be TKI naive; OR * NSCLC which harbors an EGFR T790M mutation that was acquired following progression on erlotinib, gefitinib or afatinib. This subset of patients must have not received prior third generation TKI * NOTE: EGFR mutation must be documented by a Clinical Laboratory Improvement Amendments (CLIA) certified test * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 * Measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 * Candidate for local consolidation therapy to at least one site of disease * Signed and dated written informed consent prior to admission to the study in accordance with International Council for Harmonization of Technical Requirements for Pharmaceuticals for Human Use (ICH)-Good Clinical Practice (GCP) guidelines and to the local legislation * Ability to take pills by mouth * Females of childbearing potential: * Must not be breast feeding * Must have a negative serum or urine pregnancy test * Must agree to use adequate contraception for a minimum of two weeks prior to receiving study medication until 3 months after discontinuation of the study medication * NOTE: Acceptable methods of contraception include total and true sexual abstinence, 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 sexual male partner. Females of childbearing potential are defined as those who are not surgically sterile (i.e., bilateral tubal ligation, bilateral oophorectomy, or complete hysterectomy) or postmenopausal (defined as 12 months with no menses without an alternative medical cause) * Women will be considered post-menopausal if they have been amenorrheic for the past 12 months without an alternative medical cause. The following age-specific requirements must also apply: * Women \< 50 years old: they would be considered post-menopausal if they have been amenorrheic for the past 12 months or more following cessation of exogenous hormonal treatments. The levels of luteinizing hormone (LH) and follicle-stimulating hormone (FSH) must also be in the post-menopausal range (as per the institution) * Women \>= 50 years old: they would be considered post-menopausal if they have been amenorrheic for the past 12 months or more following cessation of all exogenous hormonal treatments, or have had radiation-induced oophorectomy with the last menses \> 1 year ago, or have had chemotherapy-induced menopause with \> 1 year interval since last menses, or have had surgical sterilization by either bilateral oophorectomy or hysterectomy * Non-sterilized males who are sexually active with a female partner of childbearing potential must use adequate contraception for the duration of the study and 3 month after the last dose of study medication. Adequate contraception methods include: birth control pills (e.g. combined oral contraceptive pill), barrier protection (e.g. condom plus spermicide, cervical/vault cap or intrauterine device), and abstinence. Patients should not father a child for 6 months after completion of the study medication. Patients should refrain from donating sperm from the start of dosing until 6 months after discontinuing the study medication. If male patients wish to father children they should be advised to arrange for freezing of sperm samples prior to the start of the study medication * Life expectancy \>= 12 weeks * To be eligible for randomization, patients must: * Meet all the inclusion criteria * Have no progression of disease after 6-12 weeks of osimertinib per RECIST 1.1. To assess for progressive disease patients must have the following imaging: * Either a positron emission tomography (PET)/computed tomography (CT) scan or a CT scan of the chest/abdomen/pelvis (or CT chest) * A CT scan or a magnetic resonance imaging (MRI) of the brain * Have target lesions (lesions that will be treated with LCT if the patient is randomized to that arm). Patients that have a complete response (CR) to front-line osimertinib (e.g. no visible disease to target) will continue to be followed for progression on study but will not be randomized Exclusion Criteria: * Previous treatment with osimertinib, or a 3rd generation EGFR TKI. NOTE: Patients who are receiving initial osimertinib (6-12 weeks) outside this study are not excluded * 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 inducers of CYP3A4 (at least 3 week prior). All patients must try to avoid concomitant use of any medications, herbal supplements and/or ingestion of foods with known inducer effects on CYP3A4 * Patients with symptomatic central nervous system (CNS) metastases who are neurologically unstable * Any unresolved toxicities from prior therapy greater than Common Terminology Criteria for Adverse Events (CTCAE) grade 1 (with the exception of alopecia grade 2) at the time of starting study treatment * 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 subject to participate in the trial or which would jeopardize compliance with the protocol, or active infection including hepatitis B, hepatitis C and human immunodeficiency virus (HIV). Screening for chronic conditions is not required * 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 * Past medical history of interstitial lung disease (ILD), drug-induced ILD, radiation pneumonitis which required steroid treatment, or any evidence of clinically active interstitial lung disease * Males and females of reproductive potential who are not using and 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 * History of hypersensitivity of osimertinib (or 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 requirement * Absolute neutrophil count \< 1,500/mcL * Platelet \< 100,000/mcL * Hemoglobin \< 9.0 g/dL * Total bilirubin \> 1.5 times the upper limit of normal (ULN) if no demonstrable liver metastases or \> 3 times ULN in the presence of documented Gilbert's syndrome or liver metastases * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) \> 2.5 times ULN or \> 5 times ULN if liver metastases are present * Creatinine clearance \< 50 mL/min/1.73 m\^2 by Cockcroft-Gault equation * Any of the following cardiac criteria: * Mean resting corrected QT interval (corrected QT \[QTc\] using Fridericia's formula) \> 470 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, PR interval \> 250 msec * 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 * Patients will be excluded from randomization if they meet any of the following criteria: * Any of the exclusion criteria * Complete response to osimertinib or prior treatment to all visible lesions, such that no lesion is amenable to LCT. Note that patients can receive palliative radiation therapy prior to randomization to CNS lesions or those requiring urgent treatment (e.g. for pain or bleeding), but are only eligible for the study if they have one site amenable to further radiation therapy. In addition, these lesions will be counted towards the total number of metastases, and will also be counted as target lesions