The objective of this study is to determine if pretreatment with amifostine increases the therapeutic index of cisplatin when combined with vinblastine in the treatment of patients with Stage IIIB or 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. Antitumor efficacy will be measured in terms of survival.