Approach to model solvent in a lattice: e.g. H2O in NaCl
This is a bit outside my realm of expertise - you'd want to look at molecular dynamics (MD) simulations for more details. Let me take your question in a few parts.

1) A water molecule in a lattice is likely bound by electrostatic (and hydrogen-bond) interactions. So your general assumption is a good one.

2) MD simulations usually have a "thermostat" depending on the type of ensemble used. Your thermal energy will be distributed into different degrees of freedom, such as rotations, translations, and vibrations. So I'd work out the amount of translational free energy from statistical mechanics, and then use the electrostatic interactions to determine the path for jumps. (Your main question here seems like the activation barrier, since each lattice site should have the same energy, right?)

3) If the moves are rare, you might want to look into "rare event sampling" methods, which preserve the correct statistics, but allow you to more efficiently run your model.

Many of these techniques are already implemented in simulation codes. You might want to look at something like LAMMPS which can handle different levels of particles (e.g., atoms, molecules, crystal domains, etc.)

Hope that helps - I can only talk in broad generalities here.