Let $g$ be a Lie ring (Lie algebra over $\mathbb Z$), and let $U(g)$ and $S(g)$ denote the universal enveloping and symmetric algebra of $g$. The Poincaré-Birkhoff-Witt theorem (in the form proved by Lazard, see "Sur les algebres enveloppantes universelles de certaines algebres de Lie, M Lazard - Publ. Sci. Univ. Alger. Ser. A, 1954) yields a ring isomorphism between $S(g)$ and an associated graded of $U(g)$.
I can prove that $S(g)$ and $U(g)$ are isomorphic as $\mathbb Z$-modules; this essentially follows from the proof by Lazard. Is this already known?