A Linux container can only run on a Linux kernel (and likewise for Windows and Mac). But there are plenty of tools to more-or-less transparently solve that particular problem by e.g. running a virtual machine in the background to host a shared Linux installation that hosts the containers (and then mapping ports and stuff for you).
Wow, a Lain meme was not something I was expecting.
I should watch that show again sometime, I still have the DVDs somewhere I think.