The three-dimensional vibrational problem for the isolated binary complexes formed by the Li⁺cation with all the isotopomers of the hydrogen molecule is solved by the variational method using sufficiently exact nonempirical adiabatic surfaces of the potential energy and the dipole moment. Information on the large-amplitude vibrations was obtained for the first time, and the anharmonic effects caused by the interaction of the different internal degrees of freedom in these weakly bound van der Waals complexes were consistently taken into account. The frequencies and intensities of many spectral transitions are determined, and the average values of geometrical parameters and the dipole moment are calculated for the ground and excited vibrational states.