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)