Low Dose Daily Erlotinib in Combination With High Dose Twice Weekly Erlotinib in Patients With EGFR-Mutant Lung Cancer

The purpose of this study is to test the safety of different ways of taking erlotinib. The investigators want to find out what effects, good and/or bad, combination daily low dose and twice weekly high dose erlotinib has on the patient and lung cancer. The investigators are also seeing whether different schedules of erlotinib are better at treating lung cancer that has spread to the central nervous system. CNS expansion phase: The pulse continuous regimen will be then assess in patients with EGFR mutant lung cancers and CNS involvement. An additional expansion cohort (A) will enroll 19 patients with newly diagnosed EGFR mutant lung cancer with CNS involvement at diagnosis. The patients in the expansion cohorts will undergo the same treatment plan as the patients in the dose expansion cohort. A patient in the expansion cohorts will not be replaced if he/she does not finish the first 28 day (cycle 1) treatment period.