  Let $(\mathfrak{g},[p])$ be a finite dimensional restricted Lie algebra over
a perfect field $\mathbbm{k}$ of characteristic $p\!\ge \!3$. By combining
methods from recent work of Benson-Carlson \cite{BC20} with those of
\cite{CF21,Fa17} we obtain a description of the endotrivial
$(\mathfrak{g},[p])$-modules in case $\mathfrak{g}$ is supersolvable.
