Fundamental research on lithium ion dynamics in solids is important to develop functional materials for, e.g. sensors or energy storage systems. In many cases a comprehensive understanding is only possible if experimental data are compared with predictions from diffusion models. Nuclear magnetic resonance (NMR), besides other techniques such as mass tracer or conductivity measurements, is known as a versatile tool to investigate ion dynamics. Among the various time-domain NMR techniques, NMR relaxometry, in particular, serves not only to measure diffusion parameters, such as jump rates and activation energies, it is also useful to collect information on the dimensionality of the underlying diffusion process. The latter is possible if both the temperature and, even more important, the frequency dependence of the diffusion-induced relaxation rates of actually polycrystalline materials is analyzed. Here we present some recent systematic relaxometry case studies using model systems that exhibit spatially restricted Li ion diffusion. Whenever possible we compare our results with data from other techniques as well as current relaxation models developed for 2D and 1D diffusion. As an example, 2D ionic motion has been verified for the hexagonal form of LiBH