This command works on all distributions, including Debian, Gentoo, Mandrake and Redhat:
# cp -avx / /mnt
Proceed as described in the manual, with the modifications below:
Chapter 6 - Installing util-linux:
Apply the loop-AES patch after unpacking the sources.
Chapter 8 - Making the LFS system bootable:
Refer to Chapter 5 of this howto.