This question deserves a serious answer.
In fact it's not as trivial as the LFS FAQ would have us believe, stating simply that
any recent distribution should be fine.
However, further down the same FAQ, we find this:
GCC: Error: unrecognized option '--as-needed'
This is caused by using an incompatible host to build LFS (e.g. Fedora Core 2). The problem is caused by the fact that the host's binutils supports the "--as-needed" option, but the version of GCC we compile in LFS-5.1.1 doesn't support that option. To solve this, either use an older host, or build LFS-6.0 (currently in testing).
This problem is known to occur under Fedora Core 2, and in my case, Debian Sarge. Another poster here has reported it under Knoppix 3.6. So it would be more accurate to say that we can use any recent distribution, except for those that are too recent.
OK so there are workarounds for this particular issue, maybe use a newer version of binutils or just start again with the "testing" version of LFS. But how do I know that these workarounds won't involve (or cause) some other set of obscure problems down the line?
Checking the LFS mailing lists now, various users have reported problems building LFS under Slackware 9.0, Suse 9.1 and Debian Woody (too old!). On the other hand, Red Hat 9, Fedora Core 1 and Mandrake 10 have all been reported to build LFS successfully.
But wouldn't it be nice if someone could maintain a list of distributions that are known to work or not work with a given release of LFS? Rather than leave us all to find out for ourselves by trial and error.