We present a theoretical study of the eigenstates of the endohedral fullerene Li@C-60 for the case that the C-60 cage is assumed to be stationary. These eigenstates represent the three-dimensional nuclear dynamics of a Li atom confined to the interior of the carbon cage. The potential function employed, based on density functional theory calculations that we performed, has a variety of minima corresponding to complex hindered rotations of the Li atom in a shell about 1.5 angstrom from the cage center. The energies and wave functions of the lowest 1200 states have been calculated, and the characteristic features of selected states and the far-IR spectrum are discussed. An interesting result of the calculations is the finding that the ground-state eigenfunction can become strongly localized when the cage atoms are just slightly perturbed from icosahedral symmetry.