AZD2171 and Pemetrexed Disodium in Treating Patients With Relapsed Non-Small Cell Lung Cancer

Inclusion Criteria: * Histologically or cytologically confirmed non-small cell lung cancer * Measurable disease, defined as \>= 1 unidimensionally measurable lesion \>= 20 mm by conventional techniques or \>= 10 mm by spiral CT scan * Lesions in a previously irradiated area are considered measurable provided there has been an increase of \>= 10 mm since completion of radiotherapy * Received 1-2 prior regimens, including 1 doublet chemotherapy regimen, AND meets 1 of the following criteria: * No prior bevacizumab (cohort A) * Patients with squamous cell carcinoma, treated and controlled brain metastases, or history of hemoptysis allowed * Received 1-2 prior regimens\*, including 1 doublet chemotherapy regimen, AND meets 1 of the following criteria: * Previously treated with bevacizumab (cohort B) * No discontinuation of bevacizumab for uncontrollable hypertension and/or life-threatening bleeding * Must have disease progression after prior bevacizumab (NOTE: \*Prior adjuvant therapy is considered 1 regimen if disease progression occurred within 1 year of completion of therapy; if a regimen was discontinued within 2 courses for allergic reaction or unacceptable drug-specific toxicity, that regimen dose not count) * No large pleural effusion or ascites unless drained * No active brain metastases by brain MRI or CT scan within the past 4 weeks * Patients with treated, controlled brain metastasis allowed provided they are neurologically stable without seizures within the past 3 weeks * ECOG performance status (PS) 0-2 OR Karnofsky PS 60-100% * Absolute neutrophil count \>= 1,500/mm\^3 * Platelet count \>= 100,000/mm\^3 * WBC \>= 3,000/mm\^3 * Bilirubin =\< 1.5 times upper limit of normal (ULN) * AST and ALT =\< 2.5 times ULN (\< 5 times ULN if liver metastases present) * Creatinine normal OR creatinine clearance \>= 60 mL/min * Urine protein =\< 1+ on 2 consecutive dipsticks taken \>= 1 week apart * No significant hemorrhage (i.e., \> 30 mL in 1 episode) within the past 3 months * No significant hemoptysis (i.e., \> 5 mL fresh blood in 1 episode) within the past 4 weeks * No active gastrointestinal disease that may affect the ability of the patient to absorb AZD2171 * No history of allergic reactions attributed to compounds of similar chemical or biologic composition to AZD2171 or pemetrexed disodium * No other malignancies within the past 5 years except adequately treated basal cell or squamous cell skin cancer or carcinoma in situ * No uncontrolled intercurrent illness including, but not limited to, any of the following: * Ongoing or active infection * Symptomatic congestive heart failure * Unstable angina pectoris * Cardiac arrhythmia * Psychiatric illness or social situation that would preclude study compliance * No New York Heart Association class III or IV heart disease * Mean QTc \< 470 msec by ECG * No history of familial long QT syndrome * Fertile patients must use effective contraception * No resting blood pressure (BP) consistently \> 140/90 mm Hg; Patients whose BP is controlled after starting, adjusting, or increasing medication allowed * LVEF normal by MUGA or echocardiogram for patients at increased risk for left ventricular dysfunction, as evidenced by any of the following: * Prior treatment with anthracyclines * New York Heart Association class III or IV heart disease or controlled class II disease * Prior central thoracic radiotherapy, including radiotherapy to the heart * Myocardial infarction within the past 12 months * At least 4 weeks since prior definitive chest radiotherapy (\> 60 Gy) and recovered * At least 3 months since prior craniotomy for resection of brain metastasis * At least 3 weeks since prior radiotherapy for brain metastases * At least 4 weeks since prior chemotherapy (6 weeks for nitrosoureas or mitomycin C) and recovered * At least 2 weeks since prior palliative radiotherapy * At least 2 weeks since prior surgery (excluding the placement of vascular access or drainage of pleural effusion or ascites) and recovered * No inability or unwillingness to take folic acid, cyanocobalamin (vitamin B12), or dexamethasone * No prior pemetrexed disodium * At least 5 half-lives since prior and no concurrent drugs or biologics with proarrythmic potential including: * Amiodarone hydrochloride * Arsenic trioxide * Bepridil * Chloroquine * Chlorpromazine * Cisapride * Clarithromycin * Disopyramide * Dofetilide * Domperidone * Droperidol * Erythromycin * Halofantrine * Haloperidol * Ibutilide * Mesoridazine * Methadone * Pentamidine * Pimozide * Procainamide * Sotalol * Sparfloxacin * Thioridazine * Not pregnant or nursing * More than 30 days since prior investigational agents and recovered * No aspirin or other nonsteroidal anti-inflammatory drugs (NSAIDs) for 2 days before, during, and for 2 days after pemetrexed disodium administration: Low-dose aspirin (≤ 325 mg/day) for vascular disorders allowed * No long-acting NSAIDs (e.g., naproxen, piroxicam, diflunisal, nabumetone, or celecoxib) for 5 days before, during, and for 2 days after pemetrexed disodium * No concurrent combination antiretroviral therapy for HIV-positive patients * No other concurrent anticancer agents or therapies * No other concurrent investigational agents * Life expectancy \> 12 weeks * No concurrent medications that can markedly affect renal function (e.g., vancomycin or amphotericin) * Negative pregnancy test * Relapsed disease