Hi,
I'm not sure at what point the issue's with the i915 intel graphics will be solved and committed to a stable kernel version. But once that point arrives you can use that kernel to build LFS and be reasonably sure that once you get to BLFS' X section you will get it working. This approach doesn't deal with the liveCD (using it means using the CLI to build LFS).
Another option could be using your current distribution as host (something I normally would not suggest, but there are exceptions to the rule

). Downside to that is: You do need to make your host compliant, which can be a pain (depends on the distro used, Ubuntu is at the top but both Debian and Slackware are "easy" to make compliant).
Hope this helps.