Osimertinib in Combination With Alisertib or Sapanisertib for the Treatment of Osimertinib-Resistant EGFR Mutant Stage IIIB or IV Non-Small Cell Lung Cancer

Inclusion Criteria: * Patients must have 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 * EGFR exon 21 L858R or exon 19 deletion mutation, or T790M mutation that was acquired following treatment with first or second generation tyrosine kinase inhibitor (TKI). Eligible EGFR mutation must be confirmed by Clinical Laboratory Improvement Amendments (CLIA) certified test * Patients must have either a) disease progression on osimertinib within 30 days prior to study enrollment. Patients who continued osimertinib beyond disease progression (e.g. patients with oligo-progression who had radiation) may be eligible on further disease progression after discussion with principal investigator OR b) disease progression on osimertinib and one other line of systemic therapy (if the other systemic therapy line included PD-L1 blockade then the last dose of the latter must be more than 3 months prior to study enrollment). The number of patients who had prior osimertinib and other line of systemic therapy will be capped at 25% in each study arm * Local ablative therapy (e.g. stereotactic radiosurgery \[SRS\], stereotactic body radiation therapy \[SBRT\], or surgery) for brain or systemic metastases prior to enrollment is allowed * Measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 * Eastern Cooperative Oncology Group (ECOG) performance status…