Equivalently, is the free Lie algebra on finitely many generators over a fixed field $k$ (say of characteristic not equal to $2$) residually finite-dimensional in the sense that any nonzero element remains nonzero in some finite-dimensional quotient? Some quick Googling on my part was not successful here.

**Motivation:** If this is false, an identity holding in all finite-dimensional Lie algebras which doesn't hold in all Lie algebras isolates a potentially interesting class of infinite-dimensional Lie algebras (namely the ones satisfying the identity).