This randomized phase III trial studies carboplatin and paclitaxel to compare how well they work with or without bevacizumab and/or cetuximab in treating patients with stage IV or non-small cell lung cancer that has returned after a period of improvement (recurrent). 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. Bevacizumab may prevent the growth of new blood vessels that tumor needs to grow. Cetuximab may also stop cancer cells from growing by binding and interfering with a protein on the surface of the tumor cell that is needed for tumor growth. It is not yet known whether giving carboplatin and paclitaxel are more effective with or without bevacizumab and/or cetuximab in treating patients with non-small cell lung cancer.