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

DISEASE CHARACTERISTICS: * Diagnosis of non-small cell lung cancer (NSCLC) meeting 1 of the following criteria: * Stage IV * Stage IIIB with a malignant pleural effusion * Locally recurrent and/or persistent disease after locoregional therapy with or without systemic chemotherapy * Unidimensionally measurable disease * If the only site of measurable disease is in a previously irradiated area must have documented progression of disease in that area * No CNS metastases PATIENT CHARACTERISTICS: Age * 18 and over Performance status * ECOG 0-2 Life expectancy * Not specified Hematopoietic * Absolute neutrophil count at least 1,500/mm\^3 * Platelet count at least 100,000/mm\^3 Hepatic * Bilirubin normal * AST and ALT less than 2.5 times upper limit of normal (ULN) (if alkaline phosphatase is normal) * Alkaline phosphatase less than 4 times ULN (if AST and ALT are normal) Renal * Creatinine less than 2.0 mg/dL Other * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for 3 months after study treatment * No other malignancy within the past 5 years except curatively treated squamous cell or basal cell skin cancer or carcinoma in situ of the cervix * No diagnosis of peptic ulcer disease or gastritis/esophagitis within the past 60 days * No prior hypersensitivity to cyclooxygenase-2 (COX-2) inhibitors, nonsteroidal anti-inflammatory drugs (NSAIDs), salicylates, sulfonamides, or drugs formulated with polysorbate 80 * No pre-existing grade 2 or greater peripheral neuropathy * No concurrent medical condition that would preclude study compliance PRIOR CONCURRENT THERAPY: Biologic therapy * At least 1 week since prior biologic therapy * Phase I patients: * Any number of prior biologic therapies allowed (e.g., chimeric antibodies or kinase inhibitors) * Phase II patients: * No prior biologic therapy for recurrent/metastatic disease * No concurrent filgrastim (G-CSF) Chemotherapy * See Disease Characteristics * At least 4 weeks since prior chemotherapy * No prior irinotecan or docetaxel * Phase I patients: * Up to 2 prior chemotherapy regimens for recurrent/metastatic disease allowed (chemonaïve patients are also eligible) * Phase II patients: * At least 1 year since prior adjuvant or neoadjuvant chemotherapy for stage I-IIIA disease * No prior chemotherapy for recurrent/metastatic disease Endocrine therapy * Less than 2 weeks of cumulative oral/IV corticosteroid use within the past 3 months Radiotherapy * See Disease Characteristics * Recovered from prior radiotherapy * At least 3 weeks since prior extensive-field radiotherapy for recurrent/metastatic disease Surgery * Recovered from prior surgery Other * More than 60 days since prior treatment for peptic ulcer disease or gastritis/esophagitis * No prior NSAIDs at a frequency of more than 3 times per week for a cumulative period of more than 2 weeks within the past 30 days * No concurrent antiepileptics, cyclosporine, aspirin, or fluconazole * No concurrent NSAIDs * No other concurrent COX-2 inhibitors