In this paper we establish a Gr\"{o}bner-Shirshov bases theory for Lie
algebras over commutative rings. As applications we give some new examples of
special Lie algebras (those embeddable in associative algebras over the same
ring) and non-special Lie algebras (following a suggestion of P.M. Cohn (1963)
\cite{Conh}). In particular, Cohn's Lie algebras over the characteristic p
are non-special when p=2,3,5. We present an algorithm that one can check
for any p, whether Cohn's Lie algebras is non-special. Also we prove that any
finitely or countably generated Lie algebra is embeddable in a two-generated
Lie algebra