Docetaxel, Cisplatin, and Erlotinib Hydrochloride in Treating Patients With Stage I-III Non-small Cell Lung Cancer Following Surgery

Inclusion Criteria: * Patients must have histologically or cytologically confirmed diagnosis of stage I, II or III non-small cell lung cancer; tissue blocks or slides will be requested * Patients must have surgically resectable disease and may not be treated with prior chemotherapy or radiation * Patients must be able to tolerate systemic chemotherapy prior to surgical resection * No acute intercurrent illness or infection * Eastern Cooperative Oncology Group (ECOG) performance status 0-1 * Leukocytes \>= 3,000/uL * Absolute neutrophil count (ANC) \>= 1,500/uL * Platelets \>= 100,000/uL * Hemoglobin \>= 8g/dL * Creatinine within normal institutional limits OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Bilirubin within normal institutional limits * Alkaline phosphatase (alk phos) =\< 2.5 x upper limit of normal (ULN); if alk phos \> 2.5 x ULN but =\< 5 x ULN, patient is eligible if AST or ALT =\< ULN * Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) =\< 1.5 x ULN; if AST or ALT \> 1.5 x ULN but =\< 5 x ULN, patient is eligible if alk phos is =\< ULN * Prior to study enrollment, all women of child-bearing potential must have a negative pregnancy test; women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 2 months after the completion of t…