Inclusion Criteria:

• All patients must have pathologically determined stage IV non-small cell lung cancer (NSCLC), including stage IIIb (pleural effusion) (histology or cytology acceptable).
• Documented progression after 1 prior platinum-based chemotherapy. No more than one prior chemotherapy regimen is permitted. Patients may have also received erlotinib (before, after or concurrently with platinum based therapy).
• Patients must have measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) at least 20mm for routine CT scan and at least 10mm for spiral CT scan.
• Age at least 18 years old.
• ECOG performance status of 0-2.
• Required Laboratory Values (obtained within 30 days prior to randomization) with the following ranges:
• Hemoglobin ≥ 9.0gm/dL; transfusions permitted
• Absolute neutrophil count (ANC) ≥ 1500/mm3
• Platelet count ≥ 100,000/mm3
• International normalized ratio (INR) ≤ 1.5
• Creatinine (Cr) < 2 X the upper limit of normal (ULN)
• Alanine aminotransferase (SGOT) and aspartate aminotransferase (SGPT) < 2 X the ULN; if liver metastases are present then must be < 5 X the ULN
• Bilirubin < 2 X the ULN
• Albumin > or equal to 3.0
• Patients may have been treated with anti-EGFR kinase therapy in addition to a platinum based therapy or concurrently with platinum therapy.
• Informed Consent: Patients must be aware of the investigational nature of the therapy and provide written informed consent.
• Patients must be able to understand the requirements of the study, provide written informed consent and authorization of use and disclosure of protected health information, and agree to abide by the study restrictions and return for the required assessments.
• Women of child-bearing potential must have negative pregnancy test (serum *-HCG) with a sensitivity of at least 50 mIU/L within seven (7) days prior to the initiation of treatment and must have used effective contraception (recommended to be two reliable forms of contraception used simultaneously) or must have been sexually abstinent for at least four (4) weeks prior to the negative pregnancy test through entry in the study.
• Female patients and male patients with female partners of child-bearing potential must agree to sexual abstinence or to practice effective contraception (recommended to be two reliable forms of contraception used simultaneously). It is strongly recommended that one of the two reliable forms of contraception be non-hormonal during the entire period of apricoxib tablet treatment and for at least one (1) month after treatment is discontinued. Male patients with female sexual partners who are pregnant, possibly pregnant or who could become pregnant during the study must agree to use condoms during sexual intercourse during the entire period of apricoxib tablet treatment and for at least one (1) month after the last dose of apricoxib.

Exclusion Criteria:

• Pregnant or breast feeding due to the possible teratogenic effects of this treatment on the fetus.
• Patients are to be excluded from enrollment for known hypersensitivity to apricoxib, docetaxel, other drugs formulated with polysorbate 80, pemetrexed, sulfonamides, aspirin, or other NSAIDs.
• Radiation therapy within 2 weeks or chemotherapy within 3 weeks or non-cytotoxic investigational agents within 3 weeks of initiating study treatment or patients who have not recovered from adverse effects due to agents administered > 3 weeks prior to initiating study treatment. Screening for urinary PGE-M suppression may begin during this time period.
• Evidence of New York Heart Association class III or greater cardiac disease. History of myocardial infarction, stroke, ventricular arrhythmia, or symptomatic conduction abnormality within 12 months.
• Concurrent severe or uncontrolled medical disease (i.e., active systemic infection, diabetes, hypertension, coronary artery disease, congestive heart failure) that, in the opinion of the Investigator, would compromise the safety of the patient or compromise the ability of the patient to complete the study.
• Known HIV infection or AIDS. Testing not required.
• Symptomatic central nervous system metastases; the patient must be stable after radiotherapy for ≥ 2 weeks. Patients must be off all steroid or antiseizure medications for this indication for > 2 weeks. Patients with CNS metastases that are untreated are eligible if there is no evidence of midline shift, requirement for steroids or antiseizure medications or neurologic symptoms.
• History of upper GI bleeding, ulceration, or perforation within the past 5 years.
• Concurrent use of COX-2 inhibitors or other NSAIDs for 2 days prior to the first dose of study treatment and during study, including aspirin for 7 days prior to the first dose of study treatment and during study.
• Previous COX-2 inhibitor therapy for this diagnosis.