  Let G be a topological Kac-Moody group of rank 2 with symmetric Cartan
matrix, defined over a finite field F_q. An example is G = SL(2,F_q((t^{-1}))).
We determine a positive lower bound on the covolumes of cocompact lattices in
G, and construct a cocompact lattice \Gamma_0 < G which realises this minimum.
This completes the work begun in Part I, which considered the cases when G
admits an edge-transitive lattice.
