A semi-analytic method to compute the first coefficients of the renorm
alization group functions on a random lattice is introduced. It is use
d to show that the two-dimensional O(N) nonlinear sigma-model regulari
zed on a random lattice has the correct continuum limit. A degree kapp
a of ''randomness'' in the lattice is introduced and an estimate of th
e ratio Lambda(r)andom/Lambda(regular) for two rather opposite values
of kappa in the sigma-model is also given. This ratio turns out to dep
end on kappa.