Erlotinib and Celecoxib in Treating Patients With Stage IIIB or Stage IV Recurrent Non-Small Cell Lung Cancer

Inclusion Criteria: * Histologically or cytologically confirmed non-small cell lung cancer * Stage IIIB (malignant pleural effusion only) or IV * Recurrent disease that has progressed after 1 or 2 prior chemotherapy regimens (platinum- or nonplatinum-based) * At least 1 unidimensionally measurable lesion\* * At least 20 mm by conventional techniques OR at least 10 mm by spiral CT scan * Must have tissue specimen available for assays * No brain metastases * Performance status - ECOG 0-2 * Performance status - Karnofsky 60-100% * More than 3 months * WBC at least 3,000/mm\^3 * Absolute neutrophil count at least 1,500/mm\^3 * Platelet count at least 100,000/mm\^3 * Bilirubin normal * AST/ALT no greater than 2.5 times upper normal limit (ULN) * Creatinine normal * Creatinine clearance at least 60 mL/min * No symptomatic congestive heart failure * No unstable angina pectoris * No cardiac arrhythmia * No prior abnormalities of the cornea (e.g., dry eye syndrome or Sjögren's syndrome) * No congenital abnormality (e.g., Fuch's dystrophy) * No abnormal slit-lamp examination using a vital dye (e.g., fluorescein or Bengal-Rose) * No abnormal corneal sensitivity test (e.g., Schirmer test or similar tear production test) * Able to ingest oral medication * No requirement for IV alimentation * No history of peptic ulcer disease * No active gastrointestinal ulcers * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No other concurrent uncontrolled illness * No ongoing or active infection * No significant traumatic injury within the past 21 days * No psychiatric illness or social situation that would preclude study compliance * No prior allergic reactions to sulfonamides, aspirin, and other nonsteroidal anti-inflammatory drugs * No prior monoclonal antibodies to epidermal growth factor receptor (EGFR) * More than 4 weeks since prior chemotherapy (6 weeks for nitrosoureas or mitomycin) and recovered * No concurrent chemotherapy * No concurrent glucocorticoids * More than 4 weeks since prior radiotherapy and recovered * More than 21 days since prior major surgery * No prior surgery affecting absorption * No prior EGFR-specific tyrosine kinases * No concurrent anticonvulsants * No other concurrent investigational agents * No concurrent antiretroviral therapy for HIV-positive patients * No concurrent antacids * No concurrent administration of any of the following drugs: * Amiodarone * Chloramphenicol * Cimetidine * Fluvoxamine * Omeprazole * Zafirlukast * Clopidogrel * Cotrimoxazole * Disulfiram * Fluconazole * Fluoxetine * Fluvastatin * Fluvoxamine * Isoniazid * Itraconazole * Ketoconazole * Leflunomide * Metronidazole * Modafinil * Paroxetine * Phenylbutazone * Sertraline * Ticlopidine * Valproic acid