This randomized phase II trial studies how well erlotinib hydrochloride with or without carboplatin and paclitaxel works in treating patients with stage III-IV non-small cell lung cancer. Erlotinib hydrochloride may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy, such as carboplatin and paclitaxel, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving erlotinib hydrochloride together with carboplatin and paclitaxel may kill more tumor cells.