IIRC, and I probably don't, the LiveCD is matched to the machine it is being run on, not the target machine. I'm guessing you are going to use the LiveCD to boot the target machine so use the x86_64 version of the LiveCD.
I remastered the LiveCD to include the CLFS books and packages, but it was for the 1.0.0 version of CLFS. Nonetheless, there is a link to the remastered iso at
http://hints.cross-lfs.org/index.php...the_LFS_LiveCD