Osimertinib and Navitoclax in Treating Patients With EGFR-Positive Previously Treated Advanced or Metastatic Non-small Cell Lung Cancer

Inclusion Criteria: * Histologically confirmed non-squamous NSCLC, with incurable advanced or metastatic disease * Prior genotyping positive for an EGFR activating mutation (L858R, exon 19 deletion, G719X, L861Q) * Progression after prior treatment with an EGFR TKI; in addition to this one prior line of therapy, any additional prior lines of therapy are permitted; prior treatment with a third-generation EGFR TKI is allowed for the dose escalation phase, but is not permitted for the expansion cohort * Adequate archival tissue from a biopsy performed after progression of disease on previous EGFR TKI; or willing to undergo a new tumor biopsy prior to registration (for the dose escalation portion only this requirement can be waived if T790M status has already been determined using a local assay) * For the dose expansion portion only, patient must: 1) have a tumor which is EGFR-T790M positive and 2) be treatment naive to T790M-directed EGFR TKI (e.g. AZD9291, rociletinib, etc); T790M testing may be done locally or centrally on study, but if done locally, tissue must be available for central confirmation * Measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST 1.1) * Any number of prior therapies are allowed * Age \>= 18 years. NSCLC is exceedingly rare in patients \< 18 years of age. Because no dosing or adverse event data are currently available on the use of AZD9291 in combination with navitoclax in patients \< 18 years of age, children are excluded from th…