RATIONALE: Drugs used in chemotherapy, such as gemcitabine hydrochloride and carboplatin, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Pemetrexed disodium and celecoxib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. It is not yet known whether giving gemcitabine hydrochloride or pemetrexed disodium together with carboplatin is more effective with or without celecoxib in treating non-small cell lung cancer.