"...the goal of LFS is to build a complete and usable foundation-level system. This includes all packages needed to replicate itself."

http://linuxfromscratch.org/lfs/view/stable/prologue/package...

Buildroot's target systems don't include a compiler - it's more for real-world embedded linux system generation.

https://buildroot.org/downloads/manual/manual.html#faq-no-co...

buildroot is used to cross-compile Linux systems. It's a tool. Linux from scratch is a guide that users are supposed to follow to learn more about Linux. It's mostly an educational tool.