Patients receive anti-HGF monoclonal antibody AMG 102 (AMG 102) IV over 1 hour, pemetrexed disodium IV over 10 minutes, and cisplatin IV over 1 hour on day 1. Treatment repeats every 21 days for 6 courses in the absence of disease progression or unacceptable toxicity. Patients without disease progression may continue AMG 102 IV over 1 hour on day 1, every 3 weeks, as maintenance therapy in the absence of disease progression. Some patients undergo blood sample collection at baseline and periodically during study for correlative biomarker studies. Tumor samples from diagnostic tissue may also be analyzed.