Lie ring arising as the skew of a class two near-Lie cring

Definition
A Lie ring arising as the skew of a class two near-Lie cring is defined as a Lie ring $$L$$ such that there exists a class two near-Lie cring structure with the same underlying set and additive group structure, such that, if $$*$$ denotes the cring operation, then:

$$\! [x,y] = (x * y) - (y * x) \ \forall \ x,y \in L$$