Once LFS is build/installed you don't need the liveCD or pre-build environment anymore. All can be done from your new LFS 6.4 system.
A few tips/pointers:
- Do use the same build method as described in the LFS docs (ie: use --prefix=/x/y/z and other configure options if applicable).
- Be very careful with upgrading certain core packages (glibc, linux-headers, binutils to name a few). Best to leave these alone. You can upgrade to a newer kernel, but don't do chapter 6.7, only the steps mentioned in 8.3.
- External packages (those not covered in (B)LFS) can be installed too. It might be a good idea to also use the build method described by LFS (do take a look at the README file and do a ./configure --help to see all the options).
- Also leave the original gcc alone. If you want/need another gcc version, install it in a different location (take a look at BLFS chapter 12, especially the gcc entries).
Hope this helps.