The photoelectron spectra of LiH- and LiD- have been determined from a first principles theoretical treatment using techniques which very accurately reproduce the experimentally known electron affinity of Li and H, the equilibrium bond length and dissociation energy of LiH, and the vibrational levels of LiH (v=0-13) and LiD (v=0-8). A satisfactory simulation of the available experimental photoelectron spectra [J. Chem. Phys. 100, 1884 (1994)] can be accomplished by assuming a non-Boltzmann distribution of anion vibrational levels. A long-standing discrepancy between the experimentally determined (920+/-80 cm(-1)) and theoretically calculated (1176.1 cm(-1)) values for omega(e) of LiH- is resolved by a reassignment of the hot band transition region of the photoelectron spectrum.