A now classical result of Gerstenhaber and Shack, asserts that Simplicial cohomology is a special case of Hochshild cohomology. This result establishes that for every simplicial complex, there is an associative algebra whose Hochshild cohomology with coefficients itself is naturally isomorphic to that of the complex. In the finite case, this algebra is a poset algebra which can be represented as algebra of upper triangular matrices. But these poset algebras are also Lie algebras under the commutator bracket. What is their Lie algebra cohomology? We find that, as in the associative case, the Lie algebra cohomology of such Lie poset algebras is essentially simplicial--but the route to the result is quite different. Note: This is joint work with Murray Gerstenhaber.