It’s probably running on 30Hz. For some reason that always lags, in my experience, even on dedicated cards on desktop.
Can you check? Perhaps try with the display port adapter or a different cable or something?
I haven’t managed to get 60fps over USB-C on my 4k screen either, but I rarely use it and never bothered to check what the problem is there, and yes, it lags on the laptop while only letting me choose 30Hz, and if I explicitly choose 30 on the desktop it also lags behind but is perfectly fine on 60.