I've tested my LFS install script with version 7.3, found here:
and it works okay.
This script installs LFS using a package user method after Matthias Benkmann (section 18.104.22.168 in the book), so if that's how you install LFS then this script can save you a lot of time.
I've added an option to install as root instead of a package user, although why you would choose that option I don't know. But it's there as an alternative to jhalfs.
Perhaps more interestingly the script has the option to install LFS using systemd rather than sysvinit. The branch of that book can be found here:
If you try this I would recommend using Arch Linux as your host because it has a lot of very useful info about systemd and it gives you a good chance of understanding what is going on. There is no suggestion that LFS is going to adopt systemd anytime soon.
To get the files in github do:
git clone https://github.com/JohnBurrell/LFS-BuildScripts.git