2-Lazard-dividable Lie ring

Definition
A Lie ring $$L$$ with bracket $$[, ]$$ is termed a 2-Lazard-dividable Lie ring or a Lie ring whose bracket is the double of a Lie bracket if $$L$$ can be equipped with a Lie ring structure with the same additive group and a Lie bracket $$\{ , \}$$ such that:

$$[x,y] = 2 \{ x,y \} \ \forall \ x,y \in L$$