This randomized phase II/III trial studies how well giving maintenance chemotherapy with or without local consolidation therapy works in treating patients with stage IV non-small cell lung cancer. Drugs used in maintenance chemotherapy, such as docetaxel, pemetrexed disodium, erlotinib hydrochloride, and gemcitabine 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. Local consolidation therapy such as radiation/stereotactic body radiation or surgery may kill cancer cells left after initial treatment. Giving maintenance chemotherapy and local consolidation therapy together may work better than maintenance chemotherapy alone in treating patients with stage IV non-small cell lung cancer.