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 therapy; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Patients with a history of non-melanoma skin cancer, or other malignancies treated 5 years or more prior to the current tumor, from which the patient has remained continually disease-free, are eligible * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had prior chemotherapy or radiotherapy for lung cancer * Patients may not be receiving any other investigational agents within 30 days of trial entry, including anti-EGFR drugs * Patient has signs or symptoms of acute infection requiring systemic therapy * Patient exhibits confusion, disorientation, or has a history of major psychiatric illness that may impair patient's understanding of the informed consent * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure (New York Heart Association Functional Classification class II or worse), unstable angina pectoris, serious or clinically significant cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Patients refusing to sign the informed consent * Patients with pre-existing peripheral neuropathy National Cancer Institute (NCI) Common Toxicity Criteria (CTC) grade 2 or worse * Patients must not be pregnant or breast-feeding and all (male and female) must use a contraceptive method deemed acceptable by the investigator while receiving active treatment in the study and for up to two months following completion of therapy * Patients with a history of severe hypersensitivity reaction to Taxotere and or polysorbate 80 must be excluded