FP4 with Lineage OS here, no Gapps. Have been using it for 7 months now and everything seems to work as expected except for some of the sensors (mainly the pedometer) not being passed through to homeassistant correctly. But maybe it’s a configuration issue.
Kiwix also refuses to work correctly.
Those are very minor gripes I guess.

The setup process was surprisingly unproblematic, I had made myself ready for pain.

My main issue so far has been that the FP4 is just so enormous. No way to type comfortably in landscape mode. But maybe my thumbs are just too short. Either way this has nothing to do with LineageOS.

I’m currently using a Fairphone 4 with Lineage without problems. The battery life is good enough to last me a full day, the only weakness i noticed is the camera. I find it acceptable, but other phones in a similar price range are just better.

The other problem I initially encountered was that because Lineage didn’t officially support the Fairphone 4 until recently, I had to use an unofficial build that didn’t receive normal updates.

FP 3+ here. Apart from not being able to user certain apps because of the unlocked state of the phone, I haven’t had much trouble. I’m not sure about the FP 4 but when installing Lineage on mine, I had to explicitly tell fastboot to flash to boot_a as per step 5 in booting a custom recovery.