2-Engel and Lazard Lie ring implies class two

Statement

Suppose $L$ is a Lie ring satisfying the following two conditions: it is both a 2-Engel Lie ring (?) and a Lazard Lie ring (?). Then, $L$ must be a Lie ring of nilpotency class two (?).

Related facts

• 2-Engel and Lazard Lie group implies class two
• 2-Engel and 3-torsion-free implies class two