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-smok…