Do you have lag in all games and all platforms? It seems to be mostly restricted to NES games for me.
It's very laggy for me on all games. It's not a game breaker for slow games, such as RPGs, but for platformers and shooters it renders them pretty much unplayable. I think some of the lag comes from MFI controllers themselves, as they feel sluggish even in native Apple TV games. Provenance is worse though, it really feels very stodgy and unusable.