Erlotinib With or Without Hydroxychloroquine in Chemo-Naive Advanced NSCLC and (EGFR) Mutations

* Because no one knows which of the study options are best, participants will be randomized into of the study groups: Group A (erlotinib) or Group B (erlotinib and HCQ). Study treatment will be divided into time periods called cycles. Each study treatment cycle is 28 days. * Erlotinib (Group A and Group B) will be taken orally once a day. Hydroxychloroquine (Group B) will be taken orally once a day after taking erlotinib. * The following tests and procedures will be performed day 1 of each cycle: physical examination, performance status assessment, questions about any symptoms or side effects, blood for routine tests. The following procedures will be performed at certain study visits: Research blood tests (cycle 1, cycle 2, then every other even cycle); eye exam (cycle 4, cycle 7, and then every 3 months); assessment of the tumor with CT or MRI scan (done at the end of even cycles.