  The main technical and conceptual features of the lattice $1/N$ expansion in
the scaling region are discussed in the context of a two-parameter
two-dimensional spin model interpolating between $CP^{N-1}$ and $O(2N)$
$\sigma$ models, with standard and improved lattice actions. We show how to
perform the asymptotic expansion of effective propagators for small values of
the mass gap and how to employ this result in the evaluation of physical
quantities in the scaling regime. The lattice renormalization group $\beta$
function is constructed explicitly and exactly to $O({1/N})$.
