Hello and welcome to LinuxQuestions,
I haven't build LFS for quite some time now but I guess that it all has to do with the version of the prerequisites for building LFS version 7. Since the LiveCD is for an older version the host system requirements do not coincide with the requirements for building LFS 7. But on the other hand you can use any distro you like as a building host for LFS as long as you have the required tools with the correct versions installed. Have a look at this page
, those are the host system requirements for building LFS 7. There's even a script you can copy/paste to check if your system complies. So, install a basic distro (Debian for example), install the necessary tools (check that you're getting the mentioned versions or newer) and start building.
Looking forward to your participation in the forums. Have fun with Linux.