Although not mathematical per se, I personally like Kogut's works for Hamiltonian lattice gauge theory: there is an old RMP article and a rather good book which I purchased specifically for its presentation of the Hamiltonian theory. Of course Kogut introduced the subject along with Wilson in a PRD article, so his presentation of the material is not particularly exotic.
I will say that the advantage of the lattice is that rigor is not really much of an issue unless one wishes to take a continuous limit. Even so the incorporation of material on the Ising theory is helpful in this regard.
