Phase I-II for Patients With Recurrent or Refractory Non-small Cell Lung Cancer (NSCLC)

Inclusion Criteria: 1. Voluntary written informed consent before performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care. 2. Female subject is either post-menopausal (Postmenopausal women must be amenorrheic for at least 12 months to be considered of non-childbearing potential) or surgically sterilized or willing to use an acceptable method of birth control (i.e. a hormonal contraceptive, intra-uterine device, diaphragm with spermicide, condom with spermicide, or abstinence) for the duration of the study. Male subject agrees to use an acceptable method for contraception for the duration of the study. 3. All patients must have an Eastern Cooperative Oncology Group (ECOG)Performance Status of 0 - 2 4. Patients must have histologically or cytologically proven selected Stage IIIB (T4 lesion due to malignant pleural or pericardial effusion) or Stage IV advanced non-small cell lung cancer or recurrent disease after previous surgery and/or radiation. 5. No history of or active brain metastases 6. Patients must have measurable disease documented by computed tomography (CT) or magnetic resonance imaging (MRI). Measurable disease must be assessed within 28 days prior to registration. Pleural effusions, ascites and laboratory parameters are not acceptable as the only evidence of disease. 7. Recurrent or progressive cancer can be within a previously radiated site 8. Patients must have received one or two prior systemic therapies, one of which contained a platinum compound. No prior Bortezomib or antiangiogenic agent is permitted. Prior radiation is permitted; however, at least two weeks must have elapsed since the completion of prior radiation therapy and patients must have recovered from all associated toxicities at the time of registration. At least two weeks must have elapsed since surgery (thoracic or other major surgeries) and patients must have recovered from all associated toxicities at the time of registration. 9. Patients must have a serum creatinine \</= the institutional upper limit of normal (i.e. 1.5 mg/dL) AND a creatinine clearance \>/= 40 cc/min determined by either urine collection and testing or calculation using the following formula: Calculated Creatinine Clearance = (140 - age) \* Weight(kg) \* (0.85 if female)/ 72 \* creatinine (mg/dL) 10. Patients must have an Absolute neutrophil count (ANC)\>/= 2,000/µl and platelet count \>/= 100,000/µl obtained within 28 days prior to registration. Hemoglobin: \>9.0 \* 10\^9/L 11. Patients must have adequate hepatic function documented by a serum bilirubin \</= institutional upper limit of normal (1.0) and liver enzymes (serum glutamic oxaloacetic transaminase (SGOT) or serum glutamic pyruvic transaminase (SGPT)) \</= 3.0 \* the institutional upper limit of normal obtained within 28 days prior to registration 12. Peripheral neuropathy, if present, must be \< Grade 2 (NCI Common Terminology Criteria for Adverse Events Version 3.0). 13. Patients known to be HIV-positive and taking HAART therapy are not eligible due to possible pharmacokinetic interactions 14. Patients must not be planning to receive any other concomitant anticancer treatment including chemotherapy, radiation therapy, biologic agents or any other investigational drugs 15. Patient must be \>/= 18 years of age. 16. Patients must be informed of the investigation nature of this study and must sign and give written informed consent in accordance with institutional and federal guidelines. Exclusion Criteria: 1. Patients meeting any of the following exclusion criteria are not to be enrolled in the study. Participation in an experimental drug study within 4 weeks of the first treatment on this trial: Blood pressure \> 140/90 mm Hg, History of stroke within 6 months, Clinically significant peripheral vascular disease, Evidence of bleeding diathesis or coagulopathy, Presence of central nervous system or brain metastases 2. Major surgical procedure, open biopsy, or significant traumatic injury within 28 days prior to Day 0, or anticipation of need for major surgical procedure during the course of the study. 3. Minor surgical procedures such as fine needle aspirations or core biopsies within 7 days prior to Day 0 4. Urine protein: creatinine ratio \>/= 1.0 at screening 5. Serious non-healing wound, ulcer, or bone fracture 6. Myocardial infarction within 6 months prior to enrollment or has New York Heart Association (NYHA) Class II or heart failure, unstable angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities. Prior to study entry, and ECG abnormality at Screening has to be documented by the investigator as not medically relevant 7. Patients with squamous histology 8. Patients with hematemesis or more than ½ teaspoon of hemoptysis within 6 months of study entry. 9. Patients requiring full dose oral or parenteral anticoagulation. 10. Abdominal fistula, GI perforation, or abdominal abscess within the last 6 months 11. Patient has hypersensitivity to boron or mannitol 12. Female subject is pregnant or breast-feeding. Confirmation that the subject is not pregnant must be established by a negative serum beta-human chorionic gonadotropin (beta-hCG) pregnancy test result obtained during screening. Pregnancy testing is not required for post-menopausal or surgically sterilized women. Patient has received other investigational drugs within 28 days before enrollment 13. Serious medical or psychiatric illness likely to interfere with participation in this clinical study 14. No other prior or concurrent malignancy is allowed except for: non-melanoma skin cancers, in situ cervical cancer, and any cancer from which the patient has been disease-free for 3 years or more. 15. Pregnant or nursing women may not participate in this trial because of the increased risk of fetal harm including fetal death from the chemotherapeutic agents. Women/men of reproductive potential may not participate unless they have agreed to use an effective contraceptive method. 16. Patients requiring treatment with Nonsteroidal anti-inflammatory drugs (NSAIDS), antiplatelet agents, or aspirin \> 325 mg/day