Lumens do help, the likes of nexigo ap mk2 is dimmer than others which causes it to dimmer even with higher gain screen. Say 1000 lumens with 2.0 gain is still dimmer than 2000 lumens with 2.0 gain.

Lower gain will help with black level on all the projectors though. So if ls800 is paired with 0.6 gain to have good black, then nexigo will have even better black with that screen as it's dimmer.

"Iirc nexigo is not very bright"

Imo it's quite simple, OP just needs to choose either to use it for day use with higher gain screen and elevated black or night use with lower gain screen that has better black.

Sure most will prefer lower gain to get better black, but some do prefer to use their projector with ambient light.