  In the article the problem of the integrable classification of nonlinear
lattices depending on one discrete and two continuous variables is studied. By
integrability we mean the presence of reductions of a chain to a system of
hyperbolic equations of arbitrarily high order integrable in the Darboux sense.
Darboux integrablity admits a remarkable algebraic interpretation: the
Lie-Rinehart algebras related to both characteristic directions corresponding
to the reduced system of the hyperbolic equations have to be of finite
dimension. A classification algorithm based on the properties of the
characteristic algebra is discussed. Some classification results are presented.
