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