Cisplatin or Carboplatin, and Etoposide With or Without Sunitinib Malate in Treating Patients With Extensive-Stage Small Cell Lung Cancer

Inclusion Criteria: * All patients must have histologically or cytologically documented small cell lung cancer * Eligible disease stages: the extensive disease classification for this protocol includes all patients with disease sites not defined as limited stage; limited stage disease category includes patients with disease restricted to one hemithorax with regional lymph node metastases, including hilar, ipsilateral and contralateral mediastinal, and/or ipsilateral supraclavicular nodes; extensive stage patients are defined as those patients with extrathoracic metastatic, malignant pleural effusion, bilateral or contralateral supraclavicular adenopathy or contralateral hilar adenopathy * All patients must have measurable disease: * 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, which would make the patient not eligible, 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 * No prior chemotherapy for small cell lung cancer (SCLC) * Radiation therapy must have been completed at least one week before initiation of protocol therap…