Pemetrexed and/or Sunitinib as Second-Line Therapy in Treating Patients With Stage IIIB or Stage IV Non-small Cell Lung Cancer

Inclusion Criteria: * Histologic documentation: histologic or cytologic documentation of NSCLC * Stage: IIIB/IV with evidence of disease progression following first-line therapy * Tumor site: lung (non-small cell) * No cavitary lesions * Only one prior chemotherapy regimen in the first-line stage IIIB/IV setting is allowed; this could have been either a platinum- or non-platinum-based regimen * First-line therapy must be completed \>= 28 days before registration * Prior adjuvant therapy is allowed provided the patient had one previous regimen in the advanced stage IIIB/IV setting * At least 28 days from prior major surgery and at least 14 days from any prior radiotherapy before registration * No prior inhibitors of VEGF receptor (VEGFR) (e.g., SU5416, SU6668, AZ6474, SU11248, PTK787, AZD2171, AEE-788, sorafenib); prior treatment with epidermal growth factor receptor (EGFR) inhibitors and bevacizumab is allowed, provided at least 4 weeks has elapsed * No prior pemetrexed * Patients must have measurable or non-measurable disease * Measurable disease * Lesions that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>= 2 cm with conventional techniques or as \>= 1 cm with spiral computed tomography (CT) scan * Non-measurable disease * All other lesions, including small lesions (longest diameter \< 20 mm with conventional techniques or \< 10 mm with spiral CT scan) and truly nonmeasurable lesions * 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 * Eastern Cooperative Oncology Group (ECOG) performance status 0-1 * Pregnant or nursing mothers are not eligible for this study; patients in their child bearing years must have a baseline negative pregnancy test (in the case of females); males and females must practice appropriate contraceptive measures during the period of protocol therapy and for 6 months after completion of protocol therapy; appropriate methods of birth control include abstinence, oral contraceptives, implantable hormonal contraceptives (Norplant), or double barrier method (diaphragm plus condom) * No ongoing cardiac dysrhythmias, atrial fibrillation, or history of corrected QT interval (QTc interval) \> 500 msec (within 2 years prior to registration); the use of agents with proarrhythmic potential (e.g., quinidine, procainamide, disopyramide, sotalol, probucol, bepridil, haloperidol, risperidone, indapamide, flecainide) is not recommended while on protocol therapy * Patients with class I New York Heart Association (NYHA) heart failure are eligible; patients with a history of class II NYHA heart failure are eligible, provided they meet at least one of 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 symptomatic congestive heart failure within 12 months prior to entry are not eligible * No myocardial infarction, severe/unstable angina, coronary/peripheral artery bypass graft or stenting, cerebrovascular accident or transient ischemic attack 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 anticoagulation for thromboembolic disease are not eligible; Note: low doses of Coumadin (up to 2 mg daily) are permitted for prophylaxis of thrombosis * No history of venous thrombosis, pulmonary embolism, or hypercoagulopathy syndrome * No history of pulmonary hemorrhage, bleeding diathesis, or evidence of hemoptysis; 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 * Patients with a history of hypothyroidism or hyperthyroidism are eligible, provided they are currently euthyroid * None of the following within 28 days of beginning 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 their use is discouraged * No symptomatic or untreated central nervous system (CNS) metastases; patients with CNS metastases must be asymptomatic, must have received definitive therapy (\>= 6 weeks since resection or \>= 2 weeks since radiotherapy) for brain metastases, and be off steroids or on a stable dose for 2 weeks prior to registration * No chronic daily treatment with aspirin (\> 325 mg/day) or non-steroidal antiinflammatory agents known to inhibit platelet function; treatment with dipyridamole (Persantine), ticlopidine (Ticlid), clopidogrel (Plavix) and/or cilostazol (Pletal) is not allowed * No pleural effusions or ascites that are detectable on physical exam