if in fact
the result is the same .....
then i'm confused
I think this is the 'book' reference which you mentioned initially
archived lfs manual
i see no problem with the way it's described here.
What distro are you chrooting from?
Try something like these ( and post the output)
du -sh /
chroot $LFS du -sh /
chroot $LFS uname -a
maybe try the above with the literal value of LFS (/mnt/lfs) in place of $LFS. oR, try that with the original command.