Lie ring arising as the double of a class two Lie cring

Definition
A Lie ring arising as the double of a class two Lie cring is defined as a Lie ring $$L$$ such that there exists the structure of a class two Lie cring with the same additive group and underlying set $$L$$, such that the Lie bracket of $$L$$ is the double of the cring operation, i.e., if the cring operation is $$*$$, then:

$$[x,y] = 2(x * y) \ \forall \ x,y \in L$$