Study of Alimta® (Pemetrexed) Plus VELCADE® (Bortezomib) or Alimta Alone or VELCADE Alone in Patients With Locally Advanced or Metastatic Non-Small Cell Lung Cancer Who Have Failed Prior Therapy

Inclusion Criteria: * Men or women, 18 years of age or older * Non-small cell lung cancer (NSCLC) has been histologically or cytologically confirmed * Has relapsed or refractory locally advanced (Stage IIIb) or metastatic (Stage IV) NSCLC * Failed one prior line of systemic antineoplastic therapy for Stage IIIb/IV NSCLC (one additional prior line allowed if given as neoadjuvant, or adjuvant therapy to tumor resection) * Subject must have documented progressive disease (PD) since previous systemic antineoplastic therapy * Has measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) criteria * Has an ECOG performance status score of 0 or 1 * Has a life expectancy greater than 3 months * Female subjects must be postmenopausal (for at least 6 months), surgically sterile, abstinent, or, if sexually active, be practicing an effective method of birth control (e.g., prescription oral contraceptives, contraceptive injections, intrauterine device, double-barrier method, contraceptive patch, male partner sterilization) before entry and throughout the study; and have a negative serum or urine β-human chorionic gonadotropin (hCG) pregnancy test at screening. * Subjects (or their legally acceptable representatives) must have signed an informed consent document indicating that they understand the purpose of and procedures required for the study and are willing to and able to comply with the protocol requirements and participate in the study before any study-related procedure not part of normal medical care is conducted. * In countries where health authorities have approved the pharmacogenomic and protein testing, subjects (or their legally acceptable representatives) must have signed an informed consent for testing indicating that they agree to participate in the genetic part and protein testing part of the study; participation in the genetic and protein testing component is mandatory for testing, but optional for future research. Exclusion Criteria: * Has peripheral neuropathy of Grade 2 or greater intensity, as defined by the National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE Version 3.0) * Previous treatment with VELCADE or Alimta * Has received 2 or more prior lines of antineoplastic therapies for Stage IIIb/IV NSCLC * Any prior systemic antineoplastic therapy for NSCLC (i.e., prior chemotherapy, radiation therapy, prior monoclonal antibodies or any investigational drug or any major surgery) within 4 weeks before randomization * Has had significant weight loss (documented equal to or greater than 10% body weight in the 6 weeks before randomization) * Inadequate organ function at the screening visit as defined by the following laboratory values: * Platelet count equal to or less than 100 × 10\^9/L * Hemoglobin equal to or less than 8.0 g/dL (80 g/L) * Absolute neutrophil count (ANC) equal to or less than 1.5 × 10\^9/L * AST equal to or greater than 3 times the upper limit of the normal range (ULN) or greater than 5 times the ULN for subjects with liver metastases * ALT equal to or greater than 3 times ULN * Calculated creatinine clearance equal to or greater than 45 mL/min * Total bilirubin equal to or greater than 1.5 times ULN * Myocardial infarction within 6 months before randomization or has New York Heart Association (NYHA) Class III or IV heart failure, uncontrolled angina, severe uncontrolled arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities * Central nervous system metastasis or brain metastases that have not been completely resected or completely eliminated by radiation therapy and/or chemotherapy, or clinical or radiographic evidence that they have recurred. Subjects with a history of brain metastases are required to have had a brain computed tomography (CT) or magnetic resonance imaging (MRI) scan conducted within 1 month of enrollment to verify the continuing absence of brain metastases. * Uncontrolled pleural effusion (defined as more than 2 pleuracentesis within 4 weeks of the randomization) * Active systemic infection requiring treatment * Inability to interrupt aspirin or other nonsteroidal anti-inflammatory drugs (NSAIDs) for a 5-day period (8-day period for long-acting agents, such as piroxicam) * Unable or unwilling to take corticosteroids * Other malignancy within the past 5 years. Exceptions for the following if treated and not active: * basal cell or nonmetastatic squamous cell carcinoma of the skin; * cervical carcinoma in situ; or * International Federation of Gynecology and Obstetrics (FIGO) Stage 1 carcinoma of the cervix * History of allergic reaction attributable to compounds containing boron or mannitol * Is pregnant or breast-feeding * Currently enrolled in another clinical research study or has received an investigational agent for any reason within 4 weeks before randomization