We report the initial-state-selected and energy-resolved total reaction probabilities for the H+HLi system calculated with the aid of a time-dependent wave packet approach. The ab initio potential energy surface (PES) of Dunne [Chem. Phys. Lett. 336, 1 (2001)] is employed for the purpose. The reaction probabilities are reported for both the collinear and the three-dimensional arrangements of the reacting system. In the collinear arrangement the exothermic reaction path H+HLi-->H-2+Li is investigated only, whereas in the three-dimensional arrangement both competing reaction paths are investigated and the channel specific reaction probabilities are reported. The hydrogen exchange channel, in general, is found to be more favored over the LiH depletion channel. Both the collinear and the three-dimensional reaction probabilities reveal that the scattering occurs via resonance formation at low energies and the dynamics follows a more direct path at high energies. The overall dynamical characteristics of the system are consistent with the absence of any barrier in the underlying PES. The effect of the rotationally and vibrationally excited reactant LiH molecule on the dynamics is discussed. The importance of the noncollinear configuration of the reacting system on the LiH depletion dynamics is also delineated.