If you install lineageos from microg
then F-Droid will already be installed with system extensions and you won't need root.
then F-Droid will already be installed with system extensions and you won't need root.
You're right of course. You don't need actual superuser access to the live system to make it work (only through recovery). And, as is the case with LineageOS for MicroG, it can already be integrated into the custom OS.
Thing is, when you start doing such things, the next step is often "rooting" the device anyway, so that you can hide what is considered being "rooted" (which can be as little as running any custom OS) from APKs with "root detection" that otherwise refuse to run.