Attosecond spectroscopic techniques have made it possible to measure differences in transport times for photoelectrons from localized core levels and delocalized valence bands in solids. We report the application of attosecond pulse trains to directly and unambiguously measure the difference in lifetimes between photoelectrons born into free electron-like states and those excited into unoccupied excited states in the band structure of nickel (111). An enormous increase in lifetime of 212 +/- 30 attoseconds occurs when the final state coincides with a short-lived excited state. Moreover, a strong dependence of this lifetime on emission angle is directly related to the final-state band dispersion as a function of electron transverse momentum. This finding underscores the importance of the material band structure in determining photoelectron lifetimes and corresponding electron escape depths.