This research is being done to find out what effects, both good and/or bad, the combination of pemetrexed and sunitinib has on patients and their non-small cell lung cancer. Sunitinib is approved by the FDA for the treatment of renal cancer, however, it is experimental (investigational) in the treatment of non-small cell lung cancer. Sunitinib works by attacking both the blood vessels and the tumor cells, which starves the tumor of nutrients and slows the growth of the tumor. Pemetrexed is FDA approved for the treatment of non-small cell lung cancer patients who have progressed after prior chemotherapy treatment.