[en] Adiabatic three-dimensional potential energy and dipole moment surfaces are calculated for the ground and first excited electronic states of LiH₂⁺ including their respective atom-diatom dissociation channels as well as the complete three-atom fragmentation asymptotes. For the ground electronic state the energies of all bound rotation-vibration levels are determined variationally using the Suttcliffe-Tennyson Hamiltonian for triatomic molecules. In addition, the energy positions and widths of the low-lying quasi-bound resonances of the ground electronic state are obtained applying the stabilization method. The positions of these resonances are shown to coincide closely with the eigenvalues of an approximate Hamiltonian derived when applying the concept of the Born-Oppenheimer adiabatic separation to vibrational motions with different energy contents. The results of the present study are compared with those obtained recently for the first excited electronic state of HeH₂⁺ which has similar binding characteristics