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