Erlotinib Hydrochloride With or Without Celecoxib in Treating Patients With Stage IIIB-IV Non-Small Cell Lung Cancer

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)