Docetaxel, Cisplatin, Pegfilgrastim, and Erlotinib Hydrochloride in Treating Patients With Stage IIIB or Stage IV Non-Small Cell Lung Cancer

Inclusion Criteria: * Histologic Documentation: Either histologic or cytologic documentation of non-small cell carcinoma (NSCLC) is necessary, and the following diagnostic categories are acceptable: squamous carcinoma, basaloid carcinoma, adenocarcinoma, bronchioloalveolar carcinoma, adenosquamous carcinoma, large cell carcinoma (not neuroendocrine), sarcomatoid carcinoma, and non-small cell carcinoma not otherwise specified (NOS); histologic or cytologic documentation of recurrence is required in patients who were previously completely resected * Advanced Disease: Stage IIIB because of malignant pleural or pericardial effusion or stage IV disease * Patients must be ineligible for Avastin or decline treatment with Avastin * Prior Treatment: No prior chemotherapy or treatment with an EGFR inhibitor is allowed; brain metastasis must be under control (patient neurologically stable) * All Patients must have Measurable or Non-Measurable Disease: measurable disease is defined as at least one lesion that can be accurately measured in at least one dimension; the longest diameter of measurable lesions must be \>= 20 mm with conventional techniques or \>= 10 mm with spiral computed tomography (CT) scan; non-measurable disease includes the following: * Bone lesions * Brain metastasis or leptomeningeal disease * Ascites * Pleural/pericardial effusion * Abdominal masses that are not confirmed and followed by imaging techniques * Cystic lesions * Tumor lesions situated in a previously irradiated area * Eastern Cooperative Oncology Group (ECOG) Performance Status 0-1 * Granulocytes \>= 1,500/ul * Platelets \>= 100,000/ul * Creatinine =\< upper limit of normal (ULN) * Bilirubin =\< 1.5 mg/dl * Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) =\< 1.5 x ULN * Alkaline (Alk.) phosphatase (phos.) =\< 2.5 x ULN * Patients must provide verbal and written informed consent to participate in the study Exclusion Criteria: * Patients who are pregnant or nursing because of significant risk to the fetus/infant * Patients with neuropathy \>= grade 2 * Patients with a psychiatric illness which would prevent the patient from giving informed consent * Patients who are unable to take oral medications * Women with child-bearing potential or men who are sexual partners of women with child-bearing potential who are not willing to practice adequate contraceptive measures