Very accurate non-Born-Oppenheimer variational calculations of the ground state of e(+)LiH have been performed using explicitly correlated Gaussian functions with preexponential factors dependent on powers of the internuclear distance. In order to determine the positron detachment energy of e(+)LiH and the dissociation energy corresponding to the e(+)LiH fragmentation into HPs and Li+ we also calculated non-BO energies of HPs, LiH, and Li+. For all the systems the calculations provided the lowest ever-reported variational upper-bounds to the ground state energies. Annihilation rates of HPs and e(+)LiH were also computed. The dissociation energy of e(+)LiH into HPs and Li+ was determined to be 0.036 548 hartree. (C) 2004 American Institute of Physics.