We study the existence of post-Lie algebra structures on pairs of Lie
algebras (g,n), where one of the algebras is perfect
non-semisimple, and the other one is abelian, nilpotent non-abelian, solvable
non-nilpotent, simple, semisimple non-simple, reductive non-semisimple or
complete non-perfect. We prove several non-existence results, but also provide
examples in some cases for the existence of a post-Lie algebra structure. Among
other results we show that there is no post-Lie algebra structure on
(g,n), where g is perfect non-semisimple,
and n is sl3​(C). We also show that there is
no post-Lie algebra structure on (g,n), where
g is perfect and n is reductive with a
1-dimensional center