In Stage 1, erlotinib will be given at a starting dose of 150 milligrams (mg) by mouth (PO) once daily (QD) and the starting dose of alectinib will be 600 mg twice daily (BID), for 28 consecutive days during Cycle 1 and on Days 1 through 21 of each cycle thereafter. The starting dose of atezolizumab will be 1200 mg, administered every 3 weeks (q3W) starting on Day 8 of Cycle 1. If the starting regimen for a combination treatment is not tolerated, alternative doses and/or schedules of erlotinib and atezolizumab or alectinib and atezolizumab may be tested to determine potential recommended Phase 2 dose (RP2D) for that combination treatment. In Stage 2, a potential RP2D and schedule for each combination treatment will be investigated in an expansion cohort.