Gemcitabine Hydrochloride or Pemetrexed Disodium and Carboplatin With or Without Celecoxib in Treating Patients With Advanced Non-Small Cell Lung Cancer

DISEASE CHARACTERISTICS: * Histologically or cytologically confirmed non-small cell carcinoma of the lung, including the following cell types: * Adenocarcinoma * Large cell carcinoma * Squamous cell carcinoma * Mixture of these types * A tissue block must be available at the time of registration * Tumor expresses COX-2 (COX-2 index ≥ 2) * Stage IIIB disease with malignant pleural effusion, supraclavicular node involvement, or contralateral hilar node involvement OR stage IV disease * Patients with stage IIIB disease who are eligible for clinical trials that involve combined chemotherapy and chest irradiation are not eligible for this study * Patients with stage IV disease are eligible * Patients with recurrent disease, not amenable to (or refusing) a potentially "curative therapy," are eligible * Measurable or non-measurable disease * Measurable disease is defined as lesions that can be accurately measured in ≥ 1 dimension (longest diameter to be recorded) as ≥ 2 cm with conventional techniques or as ≥ 1 cm with spiral CT scan * Non-measurable disease is defined as all other lesions, including small lesions (longest diameter \< 20 mm with conventional techniques or \< 10 mm with spiral CT scan) and truly nonmeasurable lesions, including any of the following: * Bone lesions * Leptomeningeal disease * Ascites * Pleural/pericardial effusion * Inflammatory breast disease * Lymphangitis cutis/pulmonis * Abdominal masses that are not confirmed and followed by imaging techniques * Cystic lesions * Patients with symptomatic CNS metastases are eligible provided they received prior therapy (e.g., surgery, radiotherapy, or gamma knife), are neurologically stable, and are off steroids for ≥ 14 days before study entry * Patients with asymptomatic CNS metastases without associated edema, shift, or requirement for steroids or antiseizure medications may be eligible after discussion with the Study Chair * Patients should be off steroids at least 7 days before preregistration * No leptomeningeal disease or carcinomatous meningitis PATIENT CHARACTERISTICS: * ECOG performance status 0-2 * Granulocytes ≥ 1,500/μL * Platelet count ≥ 100,000/μL * Creatinine clearance ≥ 45 mL/min * Bilirubin ≤ 1.5 mg/dL * AST and ALT ≤ 2.0 times upper limit of normal (ULN) (≤ 5.0 times ULN if liver metastases are present) * Serum albumin ≥ 2.5 mg/dL * Not pregnant or nursing * Negative pregnancy test * No "currently active" second malignancy other than non-melanoma skin cancer * Patients are not considered to have a "currently active" malignancy if they have completed therapy and are considered by their physician to be at \< 30% risk of relapse * No known hypersensitivity to aspirin, NSAIDs, or sulfonamides * No active ulcer disease * No history of gastrointestinal bleeding within the past three years * None of the following cardiovascular conditions within the past 6 months: * Myocardial infarction * Unstable angina * Symptomatic congestive heart failure * Serious uncontrolled cardiac arrhythmia * Cerebrovascular accident or transient ischemic attack * Pulmonary embolism * Symptomatic carotid artery or peripheral vascular disease * Deep vein thrombosis * Other significant thromboembolic event PRIOR CONCURRENT THERAPY: * See Disease Characteristics * No prior chemotherapy, immunotherapy, or other systemic therapy for non-small cell lung cancer, including adjuvant therapy * At least 2 weeks since prior surgery and recovered * At least 7 days since prior radiotherapy * At least 14 days since prior NSAIDs (other than low-dose aspirin \[≤ 325 mg daily\]), including any of the following: * Celecoxib * Choline Mg * Trisalicylate (Trilisate®) * Ibuprofen (Advil® or Motrin®) * Naproxen (Aleve®, Naprosyn® or Anaprox®) * Etodolac (Lodine®) * Oxaprozin (Daypro®) * Diflunisal (Dolobid®) * Nabumetone (Relafen®) * Tolmetin (Tolectin®) * Valdecoxib (Bextra®) * No chronic use of NSAIDs (i.e., \> 4 weeks of daily use) * Patients on low-dose aspirin are eligible * No other concurrent chemotherapy or hormonal therapy (other than megestrol acetate \[Megace\] for appetite stimulation) * No other concurrent investigational therapy