Inclusion

• Pathologically proven NSCLC, stage IIIB (defined as: with pleural effusion or recurrence after mediastinal radiation and chemotherapy) or IV
• Available tumor tissue for mutation screening
• Measurable stage IIIb or IV disease by RECIST guidelines
• ECOG performance status of 0 or 1
• Progressive disease despite >= 1 prior chemotherapy regimens as standard of care or subject's refusal or inability to receive standard chemotherapy
• Normal renal function (defined as serum creatinine =< 2mg/dl)
• Normal liver function (defined as serum total bilirubin =< 1.5, and serum transaminases =< 2.5X the upper limits of normal [ULN]); if liver metastases are present, serum transaminases > 5X the ULN
• No evidence of coagulopathy (defined as PT and/or PTT =< 1.5X ULN or platelets >= 100,000)
• No evidence of leukopenia (defined as absolute neutrophil count >= 1,500 mm^3)
• Negative pregnancy test prior to initiation of treatment and adequate contraception throughout treatment

Exclusion

• Cytotoxic chemotherapy agents within 4 weeks of initiating treatment; all toxicities must be recovered to baseline or NCI CTCAE v3.0 Grade 1 from all acute effects of prior cancer treatment, except alopecia or any clinically insignificant effect, prior to study initiation
• Evidence of NYHA class III or greater cardiac disease, history of myocardial infarction, cerebral vascular accident, symptomatic ventricular arrhythmia, or symptomatic conduction abnormality
• Non-cytoxic therapy within 2 weeks of initiating treatment ; all toxicities must be recovered to baseline or NCI CTCAE v3.0 Grade 1 from all acute effects of prior cancer treatment, except alopecia or any clinically insignificant effect, prior to study initiation
• Prior radiotherapy to target lesions is not permitted unless completed more than 4 weeks prior to treatment within the study and that there has been documented progression at these sites (Radiotherapy to non-target lesions is permitted within 2 weeks of study entry provided all acute effects of the radiotherapy have resolved at least grade 1)
• Comorbid disease or a medical condition that would impair the ability of the subject to receive or comply with the study protocol
• Prior malignancy within the last 3 years with the exception of non-melanoma skin cancer or cervical cancer in situ
• Hypersensitivity of erlotinib or celecoxib or to any of the excipients of these products
• Hypersensitivity to sulfonamides, aspirin or other NSAIDS
• Prior history of EGFR inhibitor for the treatment of cancer
• Previous history of gastrointestinal ulceration, bleeding or perforation
• Concurrent use of COX-2 inhibitors or other NSAIDS (For subjects on NSAIDS prior to study initiation, cessation of the drug for 72 hours prior to study entry is required)
• Chronic or concurrent use of steroids (topical steroids are acceptable if medically indicated)
• Subjects who require treatment with fluconazole or lithium
• Any evidence of clinically active interstitial lung disease (patients with chronic stable radiographic changes who are asymptomatic need not be excluded)
• Renal insufficiency (defined as serum creatinine > 2 mg/dl)
• Liver insufficiency (defined as serum total bilirubin > 1.5, or serum transaminases > 2.5C the upper limits of normal [ULN]); if liver metastases are present, serum transaminases > 5X the ULN
• Coagulopathy (defined as PT and/or PTT > 1.5X ULN or platelets < 100,000)
• Leukopenia (defined as absolute neutrophil count < 1,500/mm^3)
• Pregnancy or inadequate contraception
• Lactating females
• Active CNS metastasis (stable, treated CNS metastasis acceptable)