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