This study will determine if pretreatment with amifostine increases the therapeutic index of cisplatin when combined with vinblastine in the treatment of patients with Stage IV non-small cell lung cancer. Increased therapeutic index is defined as increased antitumor efficacy and/or reduced toxicity (nephrotoxicity and/or neurotoxicity and/or ototoxicity) at comparable doses of cisplatin with no reduction in antitumor efficacy. Preclinical data suggest that the addition of amifostine to cisplatin and vinblastine has the potential to increase the therapeutic index of this regimen in the treatment of patients with Stage IV non-small cell lung cancer either by potentiating its antitumor activity and/or reducing the toxicity. This is the hypothesis to be tested in this Phase III trial.