Celecoxib and Docetaxel in Treating Patients With Advanced Non-Small Cell Lung Cancer

DISEASE CHARACTERISTICS: Diagnosis of stage IIIA, IIIB, or IV non-small cell lung cancer Disease progression during or after 1 or more platinum-based chemotherapy regimens Measurable or evaluable disease No symptomatic or untreated brain or leptomeningeal metastases Previously treated patients must be neurologically stable for 4 weeks after completion of appropriate therapy PATIENT CHARACTERISTICS: Age: 18 and over Performance status: SWOG 0-2 Life expectancy: Not specified Hematopoietic: Absolute neutrophil count at least 1,500/mm^3 Platelet count at least 100,000/mm^3 Hemoglobin at least 8 g/dL Hepatic: Bilirubin no greater than upper limit of normal (ULN) AST/ALT no greater than ULN (or no greater than 2.5 times ULN if alkaline phosphatase no greater than ULN) Alkaline phosphatase no greater than ULN (or no greater than 5 times ULN if AST/ALT no greater than ULN) No history of chronic hepatitis of any duration Renal: Creatinine no greater than ULN Cardiovascular: No uncontrolled congestive heart failure No uncontrolled angina No myocardial infarction and/or stroke within the past 6 months No active thromboembolic event within the past 4 weeks Gastrointestinal: No gastrointestinal bleeding within the past 6 months No history of peptic ulcer disease Other: No prior hypersensitivity reaction to docetaxel or other drugs formulated with polysorbate 80 No prior allergy to any non-steroidal anti-inflammatory drug No other prior or concurrent malignancy within the past 3 years except adequately treated squamous cell or basal cell skin cancer or carcinoma in situ of the cervix No grade 2 or greater peripheral neuropathy No active infection No other serious concurrent medical illness No history of dementia, active psychiatric disorder, or other condition that would interfere with ability to take oral medication or preclude compliance with study HIV negative Must weigh at least 50 kg (110 pounds) Not pregnant or nursing Negative pregnancy test Fertile patients must use effective barrier contraception PRIOR CONCURRENT THERAPY: Biologic therapy: Not specified Chemotherapy: See Disease Characteristics At least 4 weeks since prior chemotherapy Prior paclitaxel allowed No prior docetaxel Endocrine therapy: At least 3 days since prior steroids Radiotherapy: At least 4 weeks since prior radiotherapy No prior radiotherapy to target lesion Surgery: At least 4 weeks since prior major surgery Other: Prior intermittent use of non-steroidal anti-inflammatory drugs (NSAIDs), including rofecoxib or celecoxib, allowed At least 1 week since prior fluconazole No recent prior NSAIDs, including rofecoxib or celecoxib, for a duration of more than 30 consecutive days No concurrent fluconazole or lithium No other concurrent NSAIDs except aspirin administered at a dose of no more than 325 mg/day for cardiovascular conditions No other concurrent cyclo-oxygenase-2 inhibitors No other concurrent investigational agents