I found the following statement in Humphreys' book, 'Introduction to Lie Algebras and Representation Theory', in the first chapter, section 3.1:
"Notice that for arbitrary (Lie algebra) L, $L$ / Rad$L$ is semisimple."
And as substantiation of the statement he cites the proposition "If $I$ is a solvable ideal of a Lie algebra $L$ such that $L/I$ is solvable, then $L$ itself is solvable" which was proven earlier. I could prove the proposition that he's referring to but I could not, after hours of trying, see how the statement follows from the proposition. I'd much appreciate some help on this.