So I have downloaded the minimal LFS LiveCD and popped it into my virtual machine under VMWare Player.
As it is advertised it is definitely a valid host environment for the build process, as checked by version-check.sh
After setting up my main file systems, we need to get the source packages. There is a wget input file in the stable book download directory which comes very handy. My slow internet connection makes me have to wait for all of them to arrive.