Fluorine mobility at different structural positions in monocrystalline LaF₃ with the tysonite structure is analysed using ¹⁹F NMR line-shape analysis. The method is sensitive to ionic exchange with correlation times in the range 10^-6-10^-3 s. For the temperature range between 240 K and 400 K the motion is restricted mainly to the F^- ions in the fluorine layers perpendicular to the main symmetry axis (the F₁ sublattice), while F^- ions in the La plane (F_2,3) remain immobile. No significant anisotropy of the F₁-ionic diffusion within the layers and along the c-axis is found (D_∥c ≈ D_⊥c ≈ 6 × 10^-14 m² s^-1 at 400 K). From NMR spectra it is clear that F₁ mobility is strongly heterogeneous. The motional disorder can be described well by a broad distribution of correlation times, G(τ), which has a shape close to a log-Gaussian function and reflects the potential energy landscape in the superionic state. The variation of the centre position and width of G(τ) with temperature differs from an Arrhenius law behaviour. Ionic mobility on the microscopical scale, therefore, cannot be considered a process which is activated only thermally. Applying MD techniques shows that the presence of vacancies may lead to pronounced changes of the potential energies, and supports the idea that there is a distribution of activation energies.