Schur multiplier of Lazard Lie group and Lazard Lie ring are isomorphic

Statement
Suppose $$G$$ is a Lazard Lie group and $$L$$ is its Lazard Lie ring. Then, the Schur multiplier of $$G$$ (as a group) is isomorphic to the Schur multiplier of $$L$$ (as a Lie ring). Note that both Schur multipliers are abelian groups.