In this paper we examine the Lie derived length of a restricted universal enveloping algebra $u(L)$, where $L$ is a restricted Lie algebra over a field $F$ of characteristic $p>0$. In particular, we prove that, if the Lie derived length of $u(L)$ is at most $n$ and $p\geq 2^n$, then $L$ is abelian. Moreover, we establish when is a restricted universal enveloping algebra strongly Lie solvable and study its strong Lie derived length.
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