  A semi-analytic method to compute the first coefficients of the
renormalization group functions on a random lattice is introduced. It is used
to show that the two-dimensional $O(N)$ non-linear $\sigma$-model regularized
on a random lattice has the correct continuum limit. A degree $\kappa$ of
``randomness'' in the lattice is introduced and an estimate of the ratio
$\Lambda_{random}/\Lambda_{regular}$ for two rather opposite values of $\kappa$
in the $\sigma$-model is also given. This ratio turns out to depend on
$\kappa$.
