Docetaxel or Pemetrexed With or Without Cetuximab in Patients With Recurrent or Progressive Non-Small Cell Lung Cancer

Inclusion Criteria: * Pathologic confirmation of metastatic, unresectable, or locally-advanced NSCLC. * Disease progression during or following one prior platinum-based chemotherapy regimen for advanced disease (stage IIIB or IV). * Bidimensionally measurable disease. * Karnofsky performance status score of 60 to 100 at study entry. * The participant has tumor tissue available for immunohistochemical determination of epidermal growth factor (EGFR) expression. * Adequate recovery from recent surgery, chemotherapy, and radiation therapy. At least 4 weeks must have elapsed from major surgery, prior chemotherapy, prior treatment with an investigational agent, or prior radiation therapy (palliative radiation therapy is allowed). * Accessible for treatment and follow-up. Participants enrolled in this trial must be treated at the participating center. * Women of childbearing potential (WOCBP) and fertile men with partners of childbearing potential must be using an adequate method of contraception. * WOCBP must have a negative serum or urine pregnancy test. Exclusion Criteria: * Women who are pregnant or breastfeeding. * Dementia, altered mental status, or any psychiatric condition that would prohibit the understanding or rendering of informed consent. * A serious uncontrolled medical disorder that would impair the ability of the patient to receive protocol therapy. * Symptomatic or uncontrolled metastases in the brain. Participants receiving a glucocorticoid for brain metastases will be excluded, but those receiving anticonvulsants will be eligible. * Uncontrolled pleural effusion or ascites. * Peripheral neuropathy greater than grade 2, as assessed by the National Cancer Institutes-Common Toxicity Criteria Adverse Events (NCI-CTCAE), Version 3.0. * Any concurrent malignancy other than basal cell skin cancer, or carcinoma in situ of the cervix. Patients with a previous malignancy, but without evidence of disease for greater than or equal 3 years will be allowed to enter the trial. * More than one prior chemotherapy regimen for advanced disease. * Inadequate hematologic function defined by an absolute neutrophil count (ANC) \<1,500/mm3, a platelet count \<100,000/mm3, and a hemoglobin level \<9 g/dL. Red blood cell transfusions are not permitted within 7 days of receiving cetuximab, docetaxel, or pemetrexed. * Inadequate hepatic function, defined by a total bilirubin level \>1.5 times the upper limit of normal (ULN), aspartate transaminase (AST) and alanine aminotransferase (ALT) levels \>2.5 times the ULN (greater than or equal to 5 times the ULN if known liver metastases), and an alkaline phosphatase level \>5.0 times the ULN. * Inadequate renal function defined by a serum creatinine level \>1.5 times the ULN. * Prior treatment with cetuximab, or any other epidermal growth factor receptor inhibitors, including tyrosine kinase inhibitors, such as gefitinib or erlotinib. Participants must not have received prior chimerized or murine monoclonal antibody therapy. Prior treatment with other monoclonal antibodies targeting receptors other than the EGFR is permitted \>30 days prior to randomization. * Prior treatment with docetaxel or pemetrexed therapy. * Inability or unwillingness to take folic acid or vitamin B12 supplementation. * Inability or unwillingness to interrupt nonsteroidal anti-inflammatory drugs (NSAIDs) for a 5-day period (8-day period for long-acting agents such as piroxicam). Aspirin will be permitted during the study. * Patients (including prisoners) who are compulsorily detained (involuntarily incarcerated) for treatment of either a psychiatric or physical (eg, infectious disease) illness. * Prior treatment with an experimental drug or medical device within 30 days of randomization.