Paclitaxel and Carboplatin With or Without Celecoxib Before Surgery in Treating Patients With Stage IIIA Non-Small Cell Lung Cancer

Inclusion Criteria: * Patients with biopsy proven non-small cell lung cancer clinical stage IIIA * Mediastinoscopy positive N2 disease is mandatory * The disease must be deemed potentially resectable by the thoracic surgeon * Karnofsky performance status \> 80% * Pulmonary function must be acceptable for surgery according to institutional standards * Acceptable hepatic, renal and bone marrow function * Total serum bilirubin \< ULN * AST and/or ALT \< 2.5x ULN * Alkaline phosphatase \< 2.5x ULN * Serum creatinine \< 2.0 mg/mm3 * White blood cell \> 3000/mm3 * Platelets \> 100,000/mm3 * Age 18 or older * Willingness to abstain from chronic use of NSAIDs (defined as \> 7 days of continuous therapy per month OR defined as frequency of \> 3 times per week) for the duration of the study. For those patients on NSAIDs prior to study entry, cessation of the drug for 72 hours prior to study entry is required * Patients on low-dose ASA (\<325 mg daily) for prophylaxis of cardiovascular disease prior to study entry may remain on that dose of ASA during this trial * No anticipated chronic use of steroids. Patients may take the inhaled steroids mometasone or fluticasone if medically indicated Exclusion Criteria: * Patients with known hypersensitivity or allergic reactions to COX-2 inhibitors, sulfonamides, NSAIDs, or salicylates * Hypersensitivity to paclitaxel * Significant medical or psychiatric illness that would interfere with patient compliance * Prior malignancy within the last 3 years with the exception of non-melanoma skin cancer * Receiving other investigational agents during the course of this study or are \< 3 weeks from completion of other clinical trial therapy * Patients with a history of peptic ulcer disease, bleed disorder, irritable bowel disease, inflammatory bowel syndrome, chronic diarrhea or bowel obstruction within 5 years * Patients receiving enzyme-inducing anticonvulsants are ineligible. Patients who require concomitant therapy with NSAIDs or COX-2 inhibitors * Patients with any other serious underlying medical condition that would impair the ability of the patient to receive or comply with protocol treatment * Patients receiving lithium or fluconazole * Pregnant women or women of childbearing potential that refuse to use effective contraception during the period of chemotherapy. * Patients with a significant history of unstable cardiovascular disease * Uncontrolled diabetes mellitus or uncontrolled infection, including HIV or interstitial pneumonia or interstitial fibrosis