This is my biggest threshold in terms of technical AND tactical limitations.
The options menu only offers two "quick" function choices for combat and unit movement in general, per turn.
However, and this even applies to a PC rig, the end-of-turn calculations and movements still show significant lag and loading saves takes over 1:30 minutes for a fresh start, let alone late game.
I have this game on PC steam, and PS4 pro, on a 4k 70inch etc. But in any case, I'm stressing the point that my equipment is intended to have all features for performance turned on.
Playing on a standard map with 6 players. 5 AI. And myself. Performance-wise, it takes anywhere from 15 seconds to over a minute, with quick options turned on.
Example being turn 375 on standard play time.
My opinion is that it does lag. Not, game breaking, but, it's a long wait. So, I find myself breaking immersion by having to turn off the animations etc. Both, because even if it is playing on a maxed out machine, there's a lot of units and events going on by the end of the game...and i just don't want to be stuck watching it all.
Also, you can't have your cake and eat it too; i.e. quick enemy moves, and yours are animated.
Otherwise, this is a very impressive console version!
I prefer the controller, and I use my keyboard if I want to make a tedious map pin.
But consoles I assume equalize the lag equation in terms of your question.