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 therapy * Common Toxicity Criteria (CTC) performance status: * Phase IB: 0-1 * Phase II: 0-2 * No "currently active" second malignancy other than non-melanoma skin cancers * No history of brain metastases, spinal cord compression, or carcinomatous meningitis * No ongoing cardiac dysrhythmias, atrial fibrillation, or QTc interval \>= 500 msec; the use of agents with proarrhythmic potential (e.g., quinidine, procainamide, disopyramide, sotalol, probucol, pedridel, haloperidol, risperidone, indapamide, flecainide) is not recommended while on protocol therapy * Patients with class I New York Heart Association (NYHA) are eligible; patients with a history of class II NYHA are eligible, provided they meet the following criteria: * Patients with a history of class II heart failure who are asymptomatic on treatment * Patients with prior anthracycline exposure * Patients who have received central thoracic radiation that included the heart in the radiotherapy port * Patients with a history of class III or IV NYHA heart failure within 12 months prior to registration are not eligible * Additionally, no myocardial infarction, severe/unstable angina, coronary/peripheral artery bypass graft or stenting, cerebrovascular accident including transient ischemic attack, or pulmonary embolism within the last year * Patients with hypertension that cannot be controlled by medications (\> 150/100 mmHg despite optimal medical therapy) are not eligible * Patients who require use of therapeutic doses of coumarin-derivative anticoagulants such as warfarin are excluded, although doses of up to 2 mg daily are permitted for prophylaxis of thrombosis; Note: Low molecular weight heparin is permitted provided the patient's prothrombin time (PT) international normalized ratio (INR) is =\< 1.5 * No evidence of hemoptysis within 4 weeks prior to starting study treatment; patients with blood-tinged or blood streaked sputum will be permitted on study if the hemoptysis amounts to less than 5 mL of blood per episode and less than 10 mL of blood per 24-hour period in the best estimate of the investigator * None of the following within 28 days of treatment: abdominal fistula, gastrointestinal perforation, intra-abdominal abscess, serious or non-healing wound, ulcer, or bone fracture * The use of the following specific inhibitors and inducers of cytochrome p450, family 3, subfamily A, polypeptide 4 (CYP3A4) is not permitted; the following inhibitors of CYP3A4 are prohibited within 7 days before and during treatment with sunitinib: azole antifungals (ketoconazole, itraconazole), diltiazem, clarithromycin, erythromycin, verapamil, delavirdine, and human immunodeficiency virus (HIV) protease inhibitors (indinavir, saquinavir, ritonavir, atazanavir, nelfinavir); the following inducers of CYP3A4 are prohibited within 12 days before beginning and during treatment with sunitinib: rifampin, rifabutin, carbamazepine, phenobarbital, phenytoin, St. John's Wort, efavirenz, tipranavir * Other inhibitors and inducers of CYP3A4 may be used if necessary, but there use is discouraged * Non-pregnant and non-nursing * Granulocytes \>= 1,500/ul * Platelets \>= 100,000/ul * Creatinine clearance \>= 70 ml/min * Total bilirubin =\< 1.5 mg/dl * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 x upper limit of normal (ULN) (patients w/ liver metastases may have AST/ALT =\< 5 x ULN) * Partial thromboplastin time (PTT) =\< 1.5 x ULN