Given a Lie algebra $\mathfrak{g}$ and its univeral enveloping algebra $\mathfrak{U(g)}$ , then an element $x\in \mathfrak{U(g)}$ is called a Lie element if $x$ is in the image of $\mathfrak{g}$ in $\mathfrak{U(g)}$ .

This term is most often used for free Lie algebras and specifically in the famous Baker-Campbell-Hausdorff formula (theorem).