  Narain lattices are unimodular lattices {\it in} $\R^{r,s}$, subject to
certain natural equivalence relation and rationality condition. The problem of
describing and counting these rational equivalence classes of Narain lattices
in $\R^{2,2}$ has led to an interesting connection to binary forms and their
Gauss products, as shown in [HLOYII]. As a sequel, in this paper, we study
arbitrary rational Narain lattices and generalize some of our earlier results.
In particular in the case of $\R^{2,2}$, a new interpretation of the Gauss
product of binary forms brings new light to a number of related objects -- rank
4 rational Narain lattices, over-lattices, rank 2 primitive sublattices of an
abstract rank 4 even unimodular lattice $U^2$, and isomorphisms of discriminant
groups of rank 2 lattices.
