Summary: Let \(L\) be a finite-dimensional Lie algebra. We say a subalgebra \(H\) of \(L\) is permutably complemented in \(L\) if there is a subalgebra \(K\) of \(L\) such that \(L=H+K\) and \(H\cap K=0\). Also, if every subalgebra of \(L\) is permutably complemented in \(L\), then \(L\) is called completely factorisable. In this article, we consider the influence of these concepts on the structure of a Lie algebra, in particular, we obtain some characterizations for supersolvability of a finite-dimensional Lie algebra in terms of permutably complemented subalgebras.