Is it possible to build ‘Linux From Scratch’ (LFS) inside of an LXC container, as opposed to creating a dedicated partition per the LFS instructions?
LFS run it's own kernel. In LXC container or any container based virtualization guest system shares the host's kernel. So
LFS can't be run inside a container based VM.
Further in absence of dedicated kernel guest suffers several restrictions inside container. Like guest can't load it's own kernel module (i.e. drivers), can't drop cache etc.
Another plan may be using the host kernel and building other packages of LFS inside the host. But that's not a full featured LFS installation rather something like
chroot. Further you can't replace the existing file system as you've no access to the virtual disk while the guest is off. I believe this approach will suffer serious driver issues also, unless the LFS builder has profound experience in virtualization.
However LFS shall work fine in
xen based virtualization as they allow guest machine to run it's own Kernel.