A Study of Induction and Maintenance Treatment of Advanced Non-squamous Non-Small Cell Lung Cancer

Inclusion Criteria for the Induction Phase: * You must sign an informed consent document for clinical research. * You must have Stage IIIB or IV nonsquamous Non-Small Cell Lung Cancer. * You must at least be able to be physically mobile, take care of yourself, and must be up and about and able to perform light activities such as light housework or office work. * You are allowed to have had prior radiation therapy as long as it was not to more than 25% of the bone marrow and did not include the whole pelvis. Thoracic radiation must be completed more than 30 days before the study. You must be recovered from the toxic effects (except hair loss). * You must have at least 1 measurable tumor lesion according to the Response Evaluation Criteria in Solid Tumors (RECIST) guidelines or disease that can be evaluated by computed tomography (CT) Scan. * Your test results assessing the function of your blood forming tissue, kidneys, and liver must be satisfactory. * You must be 18 years of age or older. * Women must be sterile, postmenopausal or on contraception and men must be on contraception or sterile (e.g. post-vasectomy). Exclusion Criteria for the Induction Phase: * You cannot have squamous cell and/or mixed small cell, non-small cell lung cancer * You cannot have received other investigational drugs within the last 30 days of entering the trial. * You cannot have previously completed or withdrawn from this study or any other study investigating pemetrexed. * You cannot have other serious on-going illnesses including active infections. * You cannot have a serious cardiac condition, such as a heart attack, angina, or heart disease within 6 months of entering the trial. * You cannot have had another form of cancer other than superficial basal cell and superficial squamous (skin) cell cancer, or carcinoma in situ of the cervix within the last 5 years. Patients with a history of low-grade (Gleason score less than or equal to 6) localized prostate cancer will be eligible even if diagnosed less than 5 years ago. * You cannot have known central nervous system (CNS) metastases, other than treated, stable brain metastasis. * You cannot be receiving nor have received any prior systemic anticancer therapy for lung cancer (including chemotherapy given after surgery in early-stage treatment). * You cannot have clinically significant third-space fluid collections (e.g. ascites or pleural effusions that cannot be controlled by drainage or other procedures). * You cannot have received a recent (within 30 days) or are receiving a yellow fever vaccination. * You are unable to stop taking more than 1.3 grams of aspirin on a daily basis or other non-steroidal anti-inflammatory drugs (NSAIDs). * You are unable or unwilling to take folic acid, injections of vitamin B12, or corticosteroids. * You cannot be pregnant or breastfeeding. Inclusion criteria at Randomization for the Maintenance Phase: * You must at least be able to be physically mobile, take care of yourself, and must be up and about and able to perform light activities such as light housework or office work. * You must have documented radiographic evidence of a tumor response of complete response (CR), partial response (PR), or stable disease (SD) according to the Response Evaluation Criteria in Solid Tumors (RECIST) guidelines. Tumor assessment must occur between Cycle 4 (Day 1) of induction therapy and the date of randomization. This response does not have to be confirmed in order for the patient to be randomized to the maintenance phase.