Celecoxib and Erlotinib in Treating Former Smokers With Stage IIIB or Stage IV Non-Small Cell Lung Cancer

Criteria:

* Histologically or cytologically confirmed non-small cell lung cancer (NSCLC) meeting 1 of the following stage criteria: Stage IIIB with pleural effusion; Stage IV disease; recurrent or progressive disease after prior surgery, radiotherapy, and/or chemotherapy
* If the sole prior treatment was in the adjuvant or neoadjuvant setting, tumor progression or recurrence must have occurred within 6 months after completion of prior treatment
* Absolute neutrophil count \>= 1,500/mm\^3
* Platelet count \>= 100,000/mm\^3
* Hemoglobin \>= 10 g/dL
* Hemostasis normal
* Creatinine =\< 2.0 mg/dL
* No significant cardiovascular disease
* No New York Heart Association class III or IV cardiac disease
* No uncontrolled dysrhythmia
* No unstable angina
* No myocardial infarction within the past 6 months
* FEV1 \>= 1.0 liter OR 40% of predicted within the past 3 months
* Oxygen saturation \>= 90% on room air
* Not pregnant or nursing
* Negative pregnancy test
* Fertile patients must use effective contraception during and for 6 months after study treatment
* Willing to undergo bronchoscopy
* No allergy to sulfonamides or hypersensitivity reaction to celecoxib
* No other medical or psychological condition (e.g., acute psychosis) that would preclude study participation
* At least 4 weeks since prior chemotherapy (6 weeks for mitomycin)
* At least 4 weeks since prior radiotherapy
* Prior complete resection allowed provided there is histologic and cytologic documentation of disease recurrence
* More than 3 months since prior chemopreventative agents (e.g., oltipraz, retinoids, or N-acetylcysteine \[NAC\])
* No prior erlotinib hydrochloride
* No other prior EGFR antagonists
* No concurrent medication known to interact with erlotinib hydrochloride or celecoxib, including the following: Fluconazole, Lithium, Furosemide, Angiotensin-converting enzyme inhibitors, Phenytoin, Carbamazepine, Rifampin, Barbiturates, Hypericum perforatum (St. John's wort)
* No concurrent non-steroidal anti-inflammatory drugs
* Concurrent aspirin of up to an average dose of 325 mg/day allowed
* No aspirin treatment for 7 days prior to any bronchoscopic or skin biopsy
* No other concurrent EGFR inhibitors or cyclo-oxygenase-2 (COX-2) inhibitors
* Meets 1 of the following criteria: 1) Advanced NSCLC with at least stable disease after \>= 4 courses of platinum-containing chemotherapy 2) Relapsed or refractory disease after treatment with \>= 1 prior platinum-containing chemotherapy program, including adjuvant or neoadjuvant therapy for NSCLC
* No untreated brain metastases
* ECOG 0-1
* Former smoker, as indicated by the following: 1) At least a 30 pack-year smoking history 2) Smoking duration at least 10 years 3) At least 12 months of self-reported smoking cessation 4) Negative urine cotinine