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

This phase Ib trial studies the best dose, safety, and effect of alisertib or sapanisertib, in combination with osimertinib, in treating patients with EGFR mutated stage IIIB or IV non-small cell lung cancer that does not respond to osimertinib treatment (osimertinib resistant). Osimertinib, alisertib, and sapanisertib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. This study has two parts. The goal of part 1 of this trial is to find the highest tolerable dose of alisertib or sapanisertib in combination with osimertinib that can be safely given to patients with EGFR mutated non-small cell lung cancer. The goal of part 2 of this trial is to learn if the dose of alisertib or sapanisertib found in part 1 can help control EGFR mutated non-small cell lung cancer when given in combination with osimertinib.