It doesn't depend on the host system you build it on, in the sense that the host system is needed only because you need something to run the compilation tools etc. needed to build the new operating system.
LFS is not probably going to be what you're after, though, you'll need to do some more work with it. As I understand it, LFS is pretty much a base for an operating system; BLFS goes further, and so on. If you want udev, hotplug, desktop environments and so on, you'll have a very long route to take..