Celecoxib and Docetaxel or Pemetrexed in Treating Patients With Advanced Recurrent Non-Small Cell Lung Cancer

Eligibility Criteria: * Cytologically or histologically confirmed "COX dependent" non-small cell lung cancer. * COX dependency is defined by change in urinary PGE-M levels following a "run-in" phase of celecoxib. * Previous treatment with ≤2 different chemotherapy regimens one of which must have been platinum-based (cisplatin or carboplatin) chemotherapy. * Age ≥18 years * ECOG PS 0, 1 or 2. * Measurable or evaluable disease. * At least 3 weeks post major surgery, chemotherapy or radiotherapy \& recovered from all toxicities. * Expected survival of at least 2 months. * CNS metastases permitted provided the patient has adequately recovered from radiotherapy includes stereotactic therapy) or surgery. * Adequate renal function: serum creatinine ≤1.8 mg/dl \&/or CrCl \>50 cc/min Eligibility According to Liver Function: AST: \</= 1.5 ULN-Docetaxel; \</= 2.5 ULN-Pemetrexed (Liver parameters to be used for pemetrexed in the absence of proven or radiographically suspected liver metastases.); \</= 5.0 ULN-Pemetrexed (Liver parameters to be used for pemetrexed only in the presence of proven or radiographically suspected liver metastases.) Alk Phosphatase: \</= 2.5 ULN-Docetaxel; \</= 2.5 ULN-Pemetrexed (Liver parameters to be used for pemetrexed in the absence of proven or radiographically suspected liver metastases.); \</= 5.0 ULN-Pemetrexed (Liver parameters to be used for pemetrexed only in the presence of proven or radiographically suspected liver metastases.) Total Bilirubin: \</= 1.5 ULN-Docetaxel; \</= 1.5 ULN-Pemetrexed (Liver parameters to be used for pemetrexed in the absence of proven or radiographically suspected liver metastases.); \</= 2.5 ULN-Pemetrexed (Liver parameters to be used for pemetrexed only in the presence of proven or radiographically suspected liver metastases.) * Adequate hematologic function: ANC≥1500/mm3 \& platelets ≥100,000/mm3 * Female patients cannot be pregnant and must use contraception if of childbearing age * Lactating women are excluded. * Peripheral neuropathy must be CTC grade ≤2 * Patients must not currently be on non-steroidal anti-inflammatory agents or other COX-2 inhibitors (Must be off for at least ≤7 days) * Written informed consent. Exclusion Criteria: * More than two prior chemotherapy regimens for recurrent or relapsed NSCLC. * COX Independent as defined by change in urinary PGE-M levels following a "run-in" phase of celecoxib. * Previous treatment with both docetaxel and pemetrexed * History of greater than grade 2 allergic reaction to celecoxib or any other non-steroid anti-inflammatory agent including aspirin, ibuprofen, or indomethacin. * History of allergy to compounds containing boron or mannitol. * History of allergy to sulfonamides. * Concomitant use of Warfarin, but low dose Coumadin allowed for port prophylaxis * Recent (past 4 weeks) coronary artery bypass graft (CABG) surgery. * Inadequate organ function: * Serum creatinine ≥1.8 mg/dl or a calculated CrCl \<45 cc/min. * AST \>1.5 upper limits of normal (ULN); alkaline phosphatase \>2.5 ULN; \& bilirubin \>1.5 ULN * ANC\<1500/mm3 \& platelets \<100,000/mm3 * Active pregnancy or inability or unwillingness to employ appropriate contraception. * Small cell carcinoma histology. * Prior malignancy within 5 years of diagnosis of NSCLC. Exceptions include basal cell or non-metastatic squamous cell carcinomas of the skin, cervical carcinoma in situ or FIGO stage I cervical carcinoma, or other cancer history considered not clinically significant by the principal investigator.