About nilpotency of Leibniz algebras

Question

Some believe that if $L$ is a nilpotent Leibniz algebra and $N$ is a nilpotent ideal such that $N\subset Z^l(L)$ and $L/N$ is nilpotent then $L$ is nilpotent. In this theorem 3.1 I read a proof of this and I think is not true. I want a counterexample to show that this is not true.

Answer 1

This result follows from Theorem 5.5 of Barnes, D. (2011). Some theorems on Leibniz algebras. Comm. Algebra 39(7):2463–2472.