Pemetrexed Disodium With or Without Sorafenib as Second-Line Therapy in Treating Patients With Stage IIIB or Stage IV Non-Small Cell Lung Cancer

DISEASE CHARACTERISTICS: * Histologically or cytologically confirmed non-squamous cell non-small cell lung cancer (NSCLC) * Stage IIIB or IV disease * Squamous cell carcinomas are not allowed * Adenosquamous histology allowed * Measurable disease, defined as ≥ 1 lesion with longest diameter ≥ 2.0 cm by conventional techniques or ≥ 1.0 cm by spiral CT scan * No nonmeasurable disease only, including small lesions and truly nonmeasurable lesions, including any of the following: * Bone lesions * Leptomeningeal disease * Ascites * Pleural/pericardial effusion * Inflammatory breast disease * Lymphangitis cutis/pulmonis * Abdominal masses that are not confirmed and followed by imaging techniques * Cystic lesions * Previously treated with 1 chemotherapy regimen, including adjuvant treatment * Prior treatment with adjuvant chemotherapy is allowed and not counted as a regimen * Symptomatic pleural effusions should be drained prior to study entry * No symptomatic serosal effusion (≥ CTCAE v3.0 grade 2 dyspnea) that is not amenable to drainage prior to study entry * Stable brain metastasis allowed provided the following criteria are met: * Treated with either whole brain radiotherapy or gamma knife surgery * More than 4 weeks since prior steroids PATIENT CHARACTERISTICS: * ECOG performance status 0-1 * Life expectancy ≥ 12 weeks * Absolute neutrophil count ≥ 1,500/mm³ * Platelet count ≥ 100,000/mm³ * Hemoglobin ≥ 9 g/dL * Total bilirubin ≤ 1.5 times upper limit of normal (ULN) OR direct bilirubin normal * Creatinine clearance ≥ 45 mL/min * AST and ALT ≤ 3 times ULN (5 times ULN if liver has tumor involvement) * INR \< 1.5 OR PT/PTT normal * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for 2 weeks after completion of study treatment * Able to take folic acid, cyanocobalamin, and dexamethasone * No clinically significant infection * No known HIV positivity * No evidence or history of bleeding diathesis or coagulopathy * No serious nonhealing wound, ulcer, or bone fracture * No significant traumatic injury within the past 4 weeks * No bleeding ≥ grade 2 (except grade 2 petechiae) within the past 4 weeks * No second primary malignancy except carcinoma in situ of the cervix or nonmelanomatous skin cancer, unless malignancy was diagnosed and definitively treated ≥ 5 years ago with no subsequent evidence of recurrence * History of low-grade (Gleason score ≤ 6) localized prostate cancer allowed * Patients with a history of DCIS that has been definitively treated will be eligible even if diagnosed \< 5 years prior to registration * No other severe underlying disease or condition that, in the opinion of the investigator, would preclude study compliance or increase risk for serious adverse events * Able to swallow pills * No concurrent severe and/or uncontrolled medical conditions, including any of the following: * Uncontrolled blood pressure, defined as systolic blood pressure (BP) \> 150 mm Hg and/or diastolic BP \> 100 mm Hg, in spite of adequate antihypertensive therapy * Angina pectoris * Congestive heart failure within the past 3 months, unless LVEF \> 40% * Myocardial infarction within the past 6 months * Cardiac arrhythmia * Diabetes mellitus * Active hemoptysis PRIOR CONCURRENT THERAPY: * See Disease Characteristics * Recovered from all prior therapy, except for alopecia * No prior sorafenib tosylate or pemetrexed disodium * No prior therapy with agents that target VEGF, VEGF receptor, or VEGF receptor tyrosine kinase inhibitor (prior bevacizumab is allowed) * Prior radiotherapy allowed if all the following criteria are met: * No more than 25% of bone marrow was irradiated * Measurable disease, whether there is in-field disease progression/recurrence or disease outside the treatment fields of radiation port, is present * No acetylsalicylic acid dose of ≥ 1.3 grams/day for ≥ 10 days before and after completion of study treatment * At least 4 weeks since prior full-field radiotherapy * At least 2 weeks since prior limited-field radiotherapy * At least 4 weeks since prior major surgery (i.e., laparotomy) or open biopsy * At least 2 weeks since prior minor surgery * At least 3 weeks since prior chemotherapy (6 weeks for mitomycin C and nitrosoureas) * At least 2 weeks since prior immunotherapy, biologic therapy, or gene therapy * At least 4 weeks prior hormonal therapy * At least 4 weeks since other prior investigational agents * No concurrent antiretroviral therapy * No concurrent major surgery * No concurrent steroids * No concurrent therapeutic anticoagulation * Concurrent prophylactic anticoagulation (i.e., low-dose warfarin) of venous or arterial access devices allowed provided requirements for PT, INR, or PTT are met * No concurrent Hypericum perforatum (St. John's wort) * No concurrent grapefruit or grapefruit juice * No concurrent prophylactic use of colony-stimulating factors * No other concurrent anticancer agents or therapies