2-Engel and Lazard Lie group implies class two

Statement
Suppose $$G$$ is a group satisfying the following two conditions: it is both a fact about::2-Engel group and a fact about::Lazard Lie group. Then, $$G$$ must be a fact about::group of nilpotency class two.

Related facts

 * 2-Engel and Lazard Lie ring implies class two