Erlotinib Hydrochloride With or Without Carboplatin and Paclitaxel in Treating Patients With Stage III-IV Non-small Cell Lung Cancer

Inclusion Criteria: * Histologic documentation of primary lung adenocarcinoma including any variant thereof such as pure or mixed bronchioloalveolar carcinoma or adenosquamous cell carcinoma; patients with non-small cell lung cancer (NSCLC) not otherwise specified (NOS) are not eligible * Pathology block or unstained slides from initial or subsequent diagnosis must be available for sequencing of EGFR, K-ras, Erb-2 and B-raf; patients need to have had at least a core biopsy; patients whose diagnosis was made through a fine needle aspirate will not have sufficient material for mutational analysis and are not eligible * Select stage IIIB with cytologically documented malignant pleural or pericardial effusion OR stage IV disease * Patients must be chemotherapy naïve; they may not have received neo-adjuvant or adjuvant chemotherapy * No prior exposure to OSI-774 (erlotinib) or other treatments targeting the human epidermal growth factor receptor (HER) family axis (e.g., trastuzumab, gefitinib, cetuximab, lapatinib, etc.) * No uncontrolled central nervous system metastases (i.e., any known central nervous system \[CNS\] lesion which is radiographically unstable, symptomatic and/or requiring corticosteroids); patients must be \>= 3 weeks beyond completing cranial irradiation and off corticosteroid therapy * \>= 3 weeks since prior radiation therapy * \>= 3 weeks since prior major surgery * No treatment with an investigational agent currently or within the last 28 days * Non-smoker or former light smoker; non-smoker is defined as a person who smoked =\< 100 cigarettes in their lifetime while a former light smoker is a patient who smoked between \> 100 cigarettes AND =\< 10 pack years AND quit \>= 1 year ago; this must be documented on the On-study Form (C-1405) * Eastern Cooperative Oncology Group (ECOG) 0 or 1 * Non-pregnant and non-nursing * No dysphagia or active gastrointestinal disease or disorder that alters gastrointestinal motility or absorption; no lack of integrity of the gastrointestinal tract (e.g., a significant surgical resection of the stomach or small bowel); patients unable to swallow intact tablets must be able to swallow tablets dissolved in water * Measurable disease is defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>= 20 mm with conventional techniques or as \>= 10 mm with spiral computed tomography (CT) scan; lesions that are considered non-measurable include the following: * Bone lesions * Leptomeningeal disease * Ascites * Pleural/pericardial effusion * Lymphangitis cutis/pulmonis * Abdominal masses that are not confirmed and followed by imaging techniques * Cystic lesions * Granulocyte \>= 1,500/mcl * Platelet count \>= 100,000/mcl * Hemoglobin \>= 9.0 g/dL * Total bilirubin =\< upper limit of normal (ULN) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) =\< 2.5 x ULN * Creatinine =\< 1.5 mg/dl