Both points mentioned by spiky0011 are also valid. Have a look at the mount commands first, it might be that all is still there but not yet mounted (re-visit chapter 2 and only execute the mount command(s)).
If that doesn't solve the problem:
You mention copying files as root user, which might be a (big?) problem. All of chapter 5 is done as user lfs, which explains the permission denied messages when trying to install them.
You might try setting the permissions for all in $LFS to lfs/lfs. I'm not 100% sure that this will solve the permission denied errors, I would personally start from scratch. If you do want ti give it a try (as root user):
$ cd $LFS
chown -R lfs:lfs *
Hope this helps.