GrapheneOS is a locked-down, security-hardened system that's good if you need absolutely maximal security (e.g. journalists, activists, folks targeted by state actors). LineageOS is a more of an open system for tinkerers who want to play outside Google's walled garden.

You can have root to control your own device on Lineage, but not Graphene.

I believe you can root GrapheneOS. It just breaks the security model, so it's not recommended to do so.