Pemetrexed Disodium and Bevacizumab in Treating Patients With Stage III or Stage IV Non-Small Cell Lung Cancer

DISEASE CHARACTERISTICS: * Histologically or cytologically diagnosed stage IIIB or IV non-small cell lung cancer * Stage IIIB patients must have pleural effusion * No symptomatic serosal effusion (grade 2 dyspnea) that is not amenable to drainage * Mixed histology allowed if all components consistent with non-small cell lung cancer * Tumors with squamous cell histology feature are allowed * Must have measurable disease with at least one lesion with a longest diameter accurately measured as ≥ 2.0 cm with conventional techniques or as ≥ 1.0 cm with spiral CT * Large ( \> 4 cm) centrally located lesions or large lesions in close proximity to major blood vessels should receive palliative radiation * The irradiated lesion should not be a target lesion * Previously treated with one chemotherapy regimen in the neoadjuvant, adjuvant, or advanced disease setting * No symptomatic, untreated, or uncontrolled CNS metastases * CNS metastases treated with prior whole brain radiotherapy allowed PATIENT CHARACTERISTICS: * ECOG performance status 0-2 * Life expectancy ≥ 12 weeks * Absolute neutrophil count ≥ 1,500/mm\^3 * Platelet count ≥ 100,000/ mm\^3 * Hemoglobin ≥ 9 g/dL * Bilirubin ≤ 1.5 times upper limit of normal (ULN) or direct bilirubin normal * AST and ALT ≤ 3 times ULN (5 times ULN if liver has tumor involvement) * Creatinine clearance ≥ 45 mL/min * Urine protein:creatinine ratio \< 1.0 * Pregnant or nursing women are ineligible * Negative pregnancy test * Fertile patients must use effective contraception during and for 3 months after study participation * No seizure disorder * No clinically significant infection * No other second primary malignancy within the past 5 years except carcinoma in situ of the cervix, non-melanomatous skin cancer, or low-grade (Gleason score ≤ 6) localized prostate cancer * No hypertension or labile hypertension * No history of poor compliance with antihypertensive medications * No angina pectoris * No congestive heart failure within the past 3 months unless ejection fraction \> 40% * No myocardial infarction within the past 6 months * No cardiac arrhythmia * No interstitial pneumonia or extensive and symptomatic interstitial fibrosis of the lung * No active or recent history of hemoptysis * Hemoptysis resolved \> 2 weeks ago with measures such as palliative radiation therapy (i.e., 3,000 cGy over 10 fractions), arteriographic embolization, or endobronchial interventions (e.g., photodynamic therapy or brachytherapy) is acceptable * No diabetes * No prior serious, non-healing wounds, ulcers, or bone fractures * No history of stroke within the past 6 months * No history of abdominal fistula or gastrointestinal perforation * No intra-abdominal abscess within the past 6 months * Not at greater than average risk of bleeding * No significant traumatic injury within the past 4 weeks PRIOR CONCURRENT THERAPY: * No aspirin at doses ≥ 1.3 grams per day within 10 days prior to or 10 days after pemetrexed disodium treatment * No chemotherapy within the past 3 weeks (6 weeks for mitomycin C or nitrosoureas) * No immunotherapy or biologic therapy within the past 2 weeks * No full field radiation therapy within the past 4 weeks or limited field radiation therapy within the past 2 weeks * The site of previous radiotherapy should have evidence of progressive disease if it is the only site of disease * No prior post pelvic radiation * No prior use of pemetrexed disodium * No prior radiation to \> 25% of the marrow cavity * No major surgery (i.e., laparotomy) or open biopsy within the past 4 weeks * No minor surgery within the past 2 weeks except insertion of a vascular access device * No concurrent major surgery * No other chemotherapy, immunotherapy, hormonal therapy, radiotherapy, or any ancillary therapy considered investigational within the past 4 weeks * No concurrent use of Hypericum perforatum (St. John's wort) * No concurrent anticoagulant use * Low-dose warfarin or heparin for deep venous thrombosis prophylaxis allowed