Monoclonal antibodies, such as cetuximab and bevacizumab, can block tumor growth in different ways. Some block the ability of tumor cells to grow and spread. Others find tumor cells and help kill them or carry tumor-killing substances to them. Cetuximab may also stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Bevacizumab may stop the growth of tumor cells by blocking blood flow to the tumor. Drugs used in chemotherapy, such as paclitaxel and carboplatin, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Giving cetuximab together with paclitaxel, carboplatin, and bevacizumab may kill more tumor cells. This phase II trial is studying how well giving cetuximab together with paclitaxel, carboplatin, and bevacizumab works in treating patients with advanced non-small cell lung cancer