Study of Pralatrexate vs. Erlotinib for Non-Small Cell Lung Cancer After at Least 1 Prior Platinum-based Treatment

Inclusion Criteria: * Confirmed Stage IIIB/ IV non-small cell lung cancer (NSCLC). * Relapsed after treatment with 1 or 2 prior chemotherapy regimens, including at least 1 platinum-based treatment. Patients may have received pemetrexed as 1 of the prior therapies. Patients may not have received investigational therapy as their only prior therapy. * Recovered from the toxic effects of prior therapy. * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. * Smoked ≥ 100 cigarettes in their lifetime, whether a former or current cigarette smoker. * Adequate blood, liver and kidney function as defined by laboratory values. * Received 1-1.25 mg daily oral folic acid for at least 7 days prior to randomization and 1 mg intramuscular injection of vitamin B12 within 10 weeks prior to randomization. * Women of childbearing potential must use medically acceptable birth control and have a negative serum pregnancy test within 14 days prior to randomization. Patients who are postmenopausal for at least 1 year (\> 12 months since last menses) or are surgically sterilized do not require this test. * Men who are not surgically sterile must use medically safe and effective birth control from the time of study randomization, and agree to continue practicing until at least 90 days after the last administration of study treatment. * Accessible for repeat dosing and follow-up. * Give written informed consent. Exclusion Criteria: * Active concurrent primary malignancy (except non-melanoma skin cancer or in situ carcinoma of the cervix). If there is a history of prior malignancy, the patient must be disease-free for ≥ 5 years. Patients with other prior malignancies less than 5 years before study entry may still be enrolled if they have received treatment resulting in complete resolution of the cancer and currently have no evidence of active or recurrent disease. * Use of investigational drugs, biologics, or devices within 4 weeks prior to randomization. * Previous exposure to pralatrexate or erlotinib. * Women who are pregnant or breastfeeding. * Congestive Heart Failure Class III/IV according to New York Heart Association (NYHA) Functional Classification. * Uncontrolled hypertension. * Human immunodeficiency virus (HIV)-positive diagnosis with a CD4 count of \<100 mm3 or detectable viral load within the past 3 months, and is receiving combination anti-retroviral therapy. * Symptomatic central nervous system metastases or lesions for which treatment is required. * Major surgery within 2 weeks of study randomization. * Receipt of any conventional systemic chemotherapy within 4 weeks (6 weeks for nitrosoureas, mitomycin C), or radiation therapy (RT) within 2 weeks, prior to randomization. * Active infection or any serious underlying medical condition, which would impair the ability of the patient to receive protocol treatment. * Dementia or significantly altered mental status that would prohibit the understanding and giving of informed consent or limit study compliance.