Are you talking about mouse lag, mouse acceleration or sensitivity?
If you have really low framerates, your mouse inputs will feel unresponsive. If your frametimes are inconsistent (i.e. due to highly variable framerate), the input lag will also be inconsistent so twitch aiming and head snapping becomes really difficult to train into muscle memory.
This is one of the reasons why in competitive online fps games, people try to get insane framerates (240+) with extremely low variance between average and 0.1% lows. Consistently low input lag makes it easier to aim train.
With regards to the menus I don't know. My fps is uncapped so in menus I sit at 280 to 369 fps. It could be lag introduced by the post process effect which blurs your screen. Or it could be some holdover from a thumbstick control schema since it is designed to be a weird hybrid for control pads and mouse + keyboard users but not optimal for either. Alternatively it could just be a disconnect where the in game framerate is low, you open a menu and your mouse suddenly feels more responsive but because its so different, your muscle memory is off and you "oversteer" your cursor.