Imatinib Mesylate and Bevacizumab After First-Line Chemotherapy and Bevacizumab in Treating Patients With Stage IIIB or Stage IV Non-Small Cell Lung Cancer

DISEASE CHARACTERISTICS: * Histologically or cytologically confirmed non-small cell lung cancer * Stage IIIB (by pleural effusion only) or stage IV disease * No predominately squamous cell carcinoma * Mixed tumors will be categorized by predominant cell type * Must have completed 4 courses of platinum-based, doublet chemotherapy and bevacizumab\*, has no disease progression, and meets the following criteria: * Platinum agent may have included carboplatin or cisplatin * Second agent may have included paclitaxel, docetaxel, gemcitabine hydrochloride, vinorelbine ditartrate, or pemetrexed disodium * A change in the platinum doublet is acceptable provided the following are true: * Basis for change was toxicity rather than disease progression * Total number of courses of any platinum doublet plus bevacizumab was 4 * At least 3 of 4 courses must have included bevacizumab NOTE: \*Patients age 70 and over may have completed 4 courses of single-agent chemotherapy plus bevacizumab; single agent chemotherapy may have included paclitaxel, docetaxel, gemcitabine hydrochloride, vinorelbine ditartrate, or pemetrexed disodium * No brain metastases by brain MRI or head CT scan PATIENT CHARACTERISTICS: * ECOG performance status 0-1 * Bilirubin ≤ 1.25 times upper limit of normal (ULN) * AST and ALT ≤ 2.5 times ULN * Creatinine ≤ 1.5 times ULN * Absolute neutrophil count ≥ 1500/mm³ * Platelet count ≥ 100,000/mm³ * INR ≤ 1.5 times ULN * Urine protein:creatinine ratio ≤ 1 * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective barrier contraception during and for 3 months after completion of study treatment * No history of gross hemoptysis (defined as \> ½ teaspoon of bright red blood) * No inadequately controlled hypertension (defined as blood pressure \> 150/100 mm Hg on antihypertensive medications) * No significant traumatic injury within the past 28 days * No condition requiring continuous administration of systemic corticosteroids * No medical condition that would preclude study treatment * No medical comorbidities, including any of the following: * Unstable angina * Congestive heart failure ≥ grade 2 * Myocardial infarction within the past 6 months * Stroke within the past 6 months * Peripheral vascular disease ≥ grade 2 within the past 6 months PRIOR CONCURRENT THERAPY: * See Disease Characteristics * No prior systemic chemotherapy in the metastatic setting, except for 4 courses of platinum-based, doublet chemotherapy plus bevacizumab in the first-line setting * Prior adjuvant, neoadjuvant, or combined modality chemoradiation for localized non-small cell lung cancer allowed provided ≥ 6 months elapsed before metastatic recurrence * At least 28 days since prior major surgical procedure * No prior antiangiogenic drug, including AMG 706, CP-547, 632, vatalanib, AZD2171, thalidomide, sorafenib tosylate, or sunitinib malate * No other concurrent investigational drugs * No concurrent grapefruit juice or products containing grapefruit * No other concurrent anticancer agents, including chemotherapy and biological agents * No concurrent major surgical procedure * No concurrent therapeutic coagulation comprising warfarin, heparin, or low molecular weight heparin * Low-dose warfarin (e.g., 1 mg/day) for prophylaxis of central venous catheter thrombosis allowed * No chronic daily acetylsalicylic acid (\> 325 mg/day) or other full-dose nonsteroidal anti-inflammatory drug with antiplatelet activity