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 registr…