The reason for this study will be to find the safest maximum tolerated dose of oral vorinostat in combination with erlotinib [Tarceva (TM)] that can be given to patients with lung cancer who have relapsed or failed other therapy for the disease. Once the safest maximum tolerated dose of vorinostat is determined, patients enrolled in the clinical trial will continue vorinostat and erlotinib for up to 8 months. Safety and effectiveness will also be evaluated.