I would expect that an accurate physical model of lightning is actually a very hard problem. It's impossible to simulate directly, so you need to find an easier model. But I don't think things like magnetohydrodynamics are going to work, because it is a highly dynamical process. A phenomenological model like a random walk might produce a plausible result, but it wouldn't be very accurate. I don't know in what way it is supposed to be accurate, though.