Fibrations and coset spaces for locally compact groups

Let $G$ be a topological group and let $K,L\subseteq G$ be closed subgroups, with $K\subseteq L$. We prove that if $L$ is a locally compact pro-Lie group, then the map $q:G\mathrm{/}K\to G\mathrm{/}L$ is a fibration. As an application of this, we obtain two older results by Skljarenko, Madison and Mostert.