I actually came here for the same problem and actually realized that it was the controller deadzone in the settings that was to high and created the simulated lag response from the controller. I don't know if I even had the same lag problems described by you and all of the comments but I hope that if you try lowering the controller deadzone and increasing the sensitivity will help if you ever do see this response. I think the main menu will maybe still have a little bit of lag but increasing the sensitivity and lowering my controller deadzone completely solved the problem for me.
