I don’t know about the details, but afaik LineageOS is focused on providing (outdated) devices with up-to-date software, with privacy and security playing a minor role, while GrapheneOS is focused on privacy and security, with no longterm (3 years +) support/updates.

The article is a bit older, but imo sums up the differences between the two OSs good enough: https://pyrephone.com/de-googled-phone-comparison-e-os-vs-lineage-vs-calyx-vs-graphene/

I’m using iodéOS, which supports a few more devices than GrapheneOS and is at least known to be more secure than LineagesOS as well (article is in German only), e.g. it comes with its own antitracking solution, which I like very much.