I would strongly discourage using milk in this recipe, as it would be almost impossible to preserve. I think it might be possible to substitute milk for a VERY small percentage of the water in this recipe, but I have no idea what would be a safe percentage or whether some unusual preservation measures might be required if you used even a tiny percentage of milk.
I did a search of the swiftcraftymonkey blog, on using milk in lotions, and could find no recipes using milk. Her recipes for body "milk" and moisturizing "milk" cleanser contain to milk whatsoever.
So I think the rule would be that while milks may be used in bar soaps--even replacing all water with milk--they should not be used in either lotions or liquid soaps.