Monte Carlo simulations of the transport of Li ions on a two-dimensional lattice (n x n) are reported. The diffusion model takes explicitly into account the presence of an internal interface in the lattice. This way it is possible to model the interface glass-intercalate in a solid-state microbattery by appropriate definition of the site energies and the hopping probabilities. The ion distributions on the lattice are calculated for different initial conditions and different lattice sizes. When the required thermalization of the ions is achieved, the dependence of the mean lattice voltage on the composition x is calculated by using two different energy parameters in the definition of the site energies. Further modifications and generalizations of the model are outlined.