The pronounced difference of the conductivity relaxation time and the nuclear spin lattice relaxation time of the diffusing ion in an ionic conductor has been established as a general property observed in various glassy ionic conductors. Not so well known is the near coincidence of the conductivity relaxation time and the nuclear spin lattice relaxation time of an immobile ion bound to the glassy matrix. These two effects combined have been explained by the Coupling model and the Coulomb lattice gas model. In this work, recent published experimental results obtained on lithium thioborate glasses which exhibit two separate lithium ion motions are discussed. There is the presence of long-range diffusion of Li ions among the BS3 units as well as a localized ionic hopping motion around a BS4 unit. For the long-range diffusion motion of Li ions in the lithium thioborate glasses both effects mentioned above were observed experimentally by Li-7 and B-11 spin lattice relaxation, reaffirming that these effects are general and the details are again explainable by the Coupling model. On the other hand, for the hopping of a localized Li ion around a BS4 unit which is a new feature occurring only in the lithium thioborate glasses, the absence of interaction and correlation with other Li ions has the immediate consequence that the Coupling model will expect exactly the same Li-7 and B-11 spin lattice relaxation rate from this localized motion. This prediction for a localized Li ion around a BS4 unit, constituting a further test of the Coupling model, was indeed found experimentally and is pointed out for the first time in this work.