Pemetrexed is an FDA-approved treatment for advanced lung cancer but the response rate is still very low. Bortezomib is currently approved to treat myeloma in patients who have already been treated. Currently, multiple studies are actively investigating how well bortezomib works with other drugs. This study is testing how much bortezomib can be given to advanced lung cancer patients who have already received one treatment. This study will also see how well bortezomib and pemetrexed work together to treat lung cancer patients.

Inclusion Criteria:

• Unresectable locally advanced (Stage IIIB) or metastatic (Stage IV) NSCLC who have received one prior platinum-based chemotherapy regimen.
• One prior treatment with any biologically targeted agent is acceptable
• Stable, previously treated, brain metastases are allowed if clinically stable without steroid treatment for 10 days.
• ECOG performance status of 0 or 1.
• Measurable and/or evaluable indicator lesion(s).
• Adequate hematologic, renal and hepatic function
• Patient is of a legally consenting age
• Patient has a life-expectancy >2 months.
• Voluntary written informed consent before performance of any study-related procedure
• Female patient is either post-menopausal or surgically sterilized or willing to use an acceptable method of birth control for the duration of the study.
• Male patient agrees to use an acceptable method for contraception for the duration of the study.

Exclusion Criteria:

• Prior treatment with pemetrexed (Alimta) or Bortezomib (Velcade).
• Patient was treated for another cancer within 3 years before enrollment, with the exception of basal cell carcinoma or cervical cancer in situ.
• Peripheral neuropathy NCI grade > 2.
• Symptomatic or uncontrolled brain metastasis.
• Radiation therapy to major bone marrow (> 10% of bone marrow) areas or to target lesions within 30 days prior to study entry.
• Patient has received other investigational drugs with 14 days before enrollment.
• Serious medical or psychiatric illness likely to interfere with participation in this clinical study.
• Any systemic therapy within 21 days prior to study entry.
• Patient known to be human immunodeficiency virus (HIV)-positive.
• Patient had a significant cardiac event within 6 months of enrollment
• History of arrhythmia
• Congenital long QT syndrome or 1st degree relative with unexplained sudden death under 40 years of age.
• QT prolongation with other medications that required discontinuation of that medication.
• Presence of left bundle branch block (LBBB).
• QTc ≥480 msec or greater on screening ECG.
• Patient has hypersensitivity to bortezomib, boron or mannitol.
• Female patient is pregnant or breast-feeding.