DISEASE CHARACTERISTICS:

• Histologically or cytologically confirmed non-squamous cell histologic type non-small cell lung cancer (NSCLC)

  • Stage IIIB or IV disease

  • Mixed histology allowed if all components consistent with NSCLC

    • Tumors with squamous cell histology/features are not 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
• 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