This randomized phase II/III trial studies how well giving maintenance chemotherapy with or without stereotactic body radiation therapy works in treating patients with stage IV non-small cell lung cancer. Drugs used in maintenance chemotherapy, such as docetaxel, pemetrexed disodium, 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. Stereotactic body radiation therapy is a specialized radiation therapy that sends x-rays directly to the tumor using smaller doses over several days and may cause less damage to normal tissue. Giving maintenance chemotherapy and stereotactic body radiation therapy together may work better than maintenance chemotherapy alone in treating patients with stage IV non-small cell lung cancer.