I. To determine the safety and recommended phase II dose (RP2D) of MLN0128 (TORC1/2 inhibitor INK128) in combination with AZD9291 (EGFR inhibitor AZD9291) in patients with advanced epidermal growth factor receptor mutation positive (EGFRm) non-small cell lung cancer (NSCLC). (Dose escalation phase) II. To evaluate the safety and preliminary efficacy of MLN0128 in combination with AZD9291 in patients with advanced EGFRm NSCLC that is negative for the resistance mutation T790M (T790M negative [-]). (Dose expansion phase)