Testing Osimertinib as a Treatment for Lung Cancers With an EGFR Exon 20 Change

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)/International Association for the Study of Lung Cancer (IASLC) 7th edition staging criteria * An EGFR exon 20 insertion mutation must be detected in the tumor tissue. Patients may be enrolled in the study based on an exon 20 insertion EGFR mutation detected by any Clinical Laboratory Improvement Act (CLIA)-certified tissue assay * NOTE: Testing results are to be submitted via Medidata Rave and the study chair or delegate will review the reports * Patients must have measurable disease; baseline measurements and ALL sites of disease must be obtained within 4 weeks to registration * Patients must have previously received at least one line of therapy for their advanced lung cancer; there are no restrictions on the maximum number of prior therapies allowed * Participants must not have previously received osimertinib * Participants must have not previously received therapies targeting PDL1, PD1 or CTLA4 within 6 months (180 days) prior to registration * Age \>= 18 years * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 * Hemoglobin \>= 9.0 g/L (within 4 weeks before registration) * Leukocytes/white blood cells \>= 3,000/mcL (within 4 weeks before registration) * Absolute neutrophil count \>= 1,500/mcL (within 4 weeks before registration) * Platelets \>= 100,000/mcL (within 4 weeks before registration) * Total bilirubin =\< 1.5 x upper limit of normal (ULN) if no liver metastases or =\< 3 times ULN in the presence of documented Gilbert's syndrome (unconjugated hyperbilirubinemia) or liver metastases (within 4 weeks before registration) * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x institutional upper limit of normal; for patients with known hepatic metastases AST and/or ALT =\< 5 x ULN (within 4 weeks before registration) * Creatinine =\< 1.5 x institutional upper limit of normal (within 4 weeks before registration) * Participants may not have clinically active or symptomatic interstitial lung disease or interstitial pneumonitis (i.e., affecting activities of daily living or requiring therapeutic intervention), or a history of clinically significant interstitial lung disease or radiation pneumonitis * Participants may not have had radiation to the lung fields within four weeks (28 days) 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 treatment. At least six months (180 days) must have elapsed prior to starting treatment for radiation given with curative intent. Palliative radiotherapy to control symptoms (including gamma knife technique) is permitted. For stereotactic radiosurgery (SRS) to central nervous system (CNS) lesions, osimertinib can be held on the day of radiation only. For palliative radiotherapy (RT) to other sites of disease outside of the thorax osimertinib (osi) should be held for a minimum of 3 days before radiation and 3 days after RT is completed, but the duration of washout can be adjusted at the investigator's discretion with the approval of the study principal investigator (PI). For thoracic radiation, a 7-10 day washout period before the procedure and one week period after procedure before restarting osimertinib is advised to minimize the risk of pneumonitis. All radiotherapy related toxicities should be managed and ideally resolved before restarting osimertinib. Investigators should consider the radiotherapy when assessing causality if there are any localized adverse events (AEs) following the procedure * Participants may not have clinically symptomatic brain metastases, leptomeningeal disease, or spinal cord compression. Patients may be on a stable dose of corticosteroids to control brain metastases if they have been on a stable dose for two weeks (14 days) prior to study treatment and are clinically asymptomatic * Patients must have an ECHO or a nuclear study (MUGA or first pass) within 4 weeks (28 days) prior to registration to treatment and must not have a left ventricular ejection fraction (LVEF) \< institutional lower limit of normal (LLN). If the LLN is not defined at a site, the LVEF must be \>= 50% for the patient to be eligible * Participants may not have any of the following cardiac criteria: * Mean resting corrected QT interval (QTc) \>= 470 msec obtained from 3 electrocardiograms (ECGs) using the screening clinic ECG machine-derived QTc value * No history of QT prolongation associated with other medications that required discontinuation of that medication * Patient must not be receiving any concomitant medications that are known to be associated with Torsades de Pointes * Any clinically important abnormalities in rhythm, conduction or morphology of resting 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, 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 * Symptomatic heart failure - New York Heart Associati