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