Subvariety of variety of Lie rings containing no nontrivial perfect Lie rings contains only solvable Lie rings

First version
Suppose $$\mathcal{V}$$ is a subvariety of the variety of Lie rings such that $$\mathcal{V}$$ does not contain any nontrivial perfect Lie ring. In other words, for every nontrivial Lie ring in $$\mathcal{V}$$, the derived subring of that Lie ring is a proper subring of it.

Then, the following are true:


 * Every member of $$\mathcal{V}$$ is a solvable Lie ring.
 * Further, there is a common finite bound on the derived length of all members of $$\mathcal{V}$$. In other words, $$\mathcal{V}$$ is a subvariety of a variety of solvable Lie ring with a fixed bound on the derived length.

Second version
Suppose $$\mathcal{V}$$ is a subvariety of the variety of Lie rings that contains a non-solvable Lie ring. Then, it contains a nontrivial perfect Lie ring.

Note that this is equivalent to the first version by simple logic.

Analogues in other algebraic structures

 * Subvariety of variety of groups containing no nontrivial perfect groups contains only solvable groups