Inclusion Criteria:

1. Histologically confirmed locally advanced or metastatic NSCLC (unresectable stage IIIB or stage IV). Eligible histologies include adenocarcinoma and squamous cell carcinoma. Patients with recurrent disease after treatment for localized NSCLC are also eligible. Cytologic specimens obtained by brushings, washings, or needle aspiration are acceptable.
2. At least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as >= 20 mm with conventional techniques, or as >= 10 mm with spiral computerized tomography (CT) scan according to the Response Evaluation Criteria in Solid Tumors (RECIST).
3. Failure of at least one, and no more than two prior cytotoxic chemotherapy regimens for advanced disease (either due to progressive disease or toxicity).
4. Recovery from any toxic effects of prior therapy to <= grade 1.
5. Completion of radiation therapy at least 28 days prior to the start of study treatment (not including palliative local radiation). Previously irradiated lesions in the advanced setting cannot be included as target lesions unless clear tumor progression has been observed since the end of radiation.
6. An ECOG performance status of 0-2.
7. Absolute neutrophil count (ANC) >= 1,500, platelets >= 75,000.
8. Hemoglobin >= 9 g/dL (within 7 days prior to study treatment). Patients may be transfused or receive erythropoietin to maintain or exceed this level where otherwise indicated.
9. International normalized ratio (INR) <= 1.5 or prothrombin time (PT)/partial thromboplastin time (PTT) within normal limits (WNL) of the institution (if patients are not on anti-coagulation therapy. Patients receiving anti-coagulation treatment with an agent such as warfarin or heparin may be allowed to participate with the therapeutic range established prior to study treatment initiation).
10. Serum creatinine <= 1.5 x institutional upper limit of normal (ULN) within 7 days prior to study treatment. If the absolute value is greater than 2 mg/dL, the creatinine clearance.
11. Transaminases <= 3 x institutional ULN (except if there is known hepatic metastasis, wherein transaminases may be >= 5 x institutional ULN).
12. Patients must be able to understand the nature of this study, give written informed consent, and comply with study requirements.
13. Agreement of female patients of childbearing potential and male patients who have partners of childbearing potential to use an effective form of contraception to prevent pregnancy during treatment, and for a minimum of 90 days thereafter.
14. Patients who have treated brain metastases >= 4 weeks out (with surgery and/or radiation therapy) and no evidence of CNS progression.

Exclusion Criteria:

1. Past or current history of neoplasm (other than the entry diagnosis), with the exception of treated non-melanoma skin cancer or carcinoma in-situ of the cervix, or other cancers cured by local therapy alone, and a disease-free survival (DFS) >= 3 years.
2. Patients who have mixed tumors with small-cell elements are ineligible.
3. Pregnancy or lactation. All females of child-bearing potential must have negative serum or urine pregnancy tests within 7 days prior to study treatment.
4. Prior treatment with EGFR TKIs or VEGFR TKIs for NSCLC. [NOTE: prior cetuximab and/or bevacizumab use is permitted].

5. Significant cardiac disease within 90 days of starting study treatment, including:

   • superior vena cava syndrome
   • new onset angina
   • congestive heart failure (CHF) > Class 2 per New York Heart Association (NYHA) classification
   • arrhythmia
   • valvular heart disease
6. Myocardial infarction within 6 months prior to initiation of study treatment.
7. Cardiomegaly on chest imaging or ventricular hypertrophy on electrocardiogram (ECG), unless the left ventricular ejection fraction (LVEF) is within normal range for the institution.
8. Poorly controlled hypertension (defined as systolic blood pressure [BP] >150 mm Hg and/or diastolic blood pressure >100 mm Hg on anti-hypertensive medications).
9. Unstable angina (anginal symptoms at rest).
10. Cardiac ventricular arrhythmias requiring anti-arrhythmic therapy.
11. Presence of cardiac disease that, in the opinion of the investigator, increases the risk of ventricular arrhythmia.
12. A serious active infection (> grade 2) at the time of treatment.
13. A serious underlying medical condition that would impair the ability of the patient to receive protocol treatment.
14. Untreated brain metastases.
15. A major surgical procedure, open biopsy, or significant traumatic injury within 28 days of beginning treatment, or anticipation of the need for major surgery during the course of the study.
16. Stroke or transient ischemic attack (TIA) within the past 6 months.
17. Any prior history of hypertensive crisis or hypertensive encephalopathy.
18. Pulmonary hemorrhage/bleeding event >= grade 2 within 28 days of study treatment.
19. Any other non-pulmonary hemorrhage/bleeding event >= grade 3 within 28 days of study treatment.
20. Evidence or history of bleeding diathesis or coagulopathy.
21. Serious non-healing wound, ulcer, or bone fracture.
22. Use of St. John's Wort or rifampin (rifampicin).
23. Known or suspected allergy/hypersensitivity to any agent given in the course of this trial.
24. Patients with gastrointestinal (GI) tract disease, causing the inability to take oral medication, malabsorption syndrome, a requirement for IV alimentation, prior surgical procedure affecting absorption, uncontrolled inflammatory GI disease (e.g., Crohn's ulcerative colitis).
25. Any condition that impairs the patient's ability to swallow whole pills.