Is it educational to do this on a VM or should I break out my old thinkpad?

Both. Whatever works for you I'd say. I targeted the Raspberry Pi (Cross-Linux From Scratch variant), and a fake root (via chroot) and qemu. This was circa 2014 though.

These days the ARM64 processor on the Raspberry Pi 5 is probably fast enough to just build natively on it, no cross-compilation necessary. Cross-compiling adds a metric ton of complexity.

Having done this way back when on both: go with a VM first.

Targeting a known set of virtual devices makes a lot of things much easier when building LFS. Dev ux is also much nicer:, you get faster restarts, a socket and optional snapshots to go back to a known less broken state.

In my opinion having it on a separate computer is easier, but you can also run this in one or three KDE konsole tabs, for instance, on an external hdd/sdd.