Characteristic subgroup of additive group of a Lie ring

Definition
Suppose $$L$$ is a Lie ring and $$S$$ is a subset of $$L$$. We say that $$S$$ is a characteristic subgroup of (the) additive group of $$L$$ if $$S$$ is a defining ingredient::characteristic subgroup of the abelian group defined as the underlying additive group of $$L$$.