  We study five different types of the homology of a Lie algebra over a
commutative ring which are naturally isomorphic over fields. We show that they
are not isomorphic over commutative rings, even over $\mathbb Z,$ and study
connections between them. In particular, we show that they are naturally
isomorphic in the case of a Lie algebra which is flat as a module. As an
auxiliary result we prove that the Koszul complex of a module $M$ over a
principal ideal domain that connects the exterior and the symmetric powers
$0\to \Lambda^n M\to M \otimes \Lambda^{n-1} M \to \dots \to S^{n-1}M \otimes M
\to S^nM\to 0 $ is purely acyclic.
