RATIONALE: 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. Monoclonal antibodies, such as 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. Bevacizumab may also stop the growth of non-small cell lung cancer by blocking blood flow to the tumor. Pemetrexed disodium may stop the growth of tumor cells by blocking some enzymes needed for cell growth. It is not yet known whether giving bevacizumab or pemetrexed disodium alone or in combination is more effective in treating non-squamous non-small cell lung cancer.