Li-7 and Li-6 nuclear magnetic resonance (NMR) experiments are carried out on the perovskite Li3xLa1/3-xNbO3. The results are compared to those obtained on the titanate Li3xLa2/3-xTiO3 (LLTO) in order to investigate the effect, on the lithium ion dynamics, of the total substitution of Nb5+ for Ti4+ in the B-site of the ABO(3) perovskites. The XRD patterns analysis reveals that this substitution leads to a change in the distribution of the La3+ ions in the structure. La3+ ions distribution is very important, in regard to ionic conductivity, because these immobile ions can be considered as obstacles for the long-range Li+ motion. If compared to the titanates, the compounds of the niobate solid solution have a bigger unit cell volume, a smaller number of La3+ ions, and a higher number of vacancies. These should favor the motion of the mobile ions into the structure. This is not experimentally observed. Therefore, the interactions between the mobile species and their environment greatly influence their mobility. Li-7 and Li-6 NMR relaxation time experiments reveal that the Li relaxation mechanism is not dominated by quadrupolar interaction. Li-7 NMR spectra reveal the presence of different Li+ ion sites. Some Li+ ions reside in an isotropic environment with no distortion, some others reside in weakly distorted environments. T-1, Tip, and T-2 experiments allow us to evidence two motions of Li+. As in LLTO, T-1 probes a fast motion of the Li+ ions inside the A-cage of the perovskite structure and T-1p a slow motion of these ions from A-cage to A-cage. At variance with what has been observed in LLTO, these different Li+ ions can be differentiated through the spin-lattice relaxation times, T-1 and T-1p, as well as through the transverse relaxation time, T-2.