First go to clipboard, setup, controls, joystick, and get the screen up that shows the axis. See if there's a lag in the square box that shows current input. If there is, it could be a windows problem or a joystick problem.
I would try in the Windows calibration screen, under start, control panel, gameport (or is it under gamepad? It's easy to spot) and then select the test screen (not the calibrate). Move it around, see if there is, in fact, a lag. If there is, then try new drivers, or reinstall current drivers. Perhaps the device itself is going south, and needs to be replaced. If you have an old, cheap, spare stick try it as well. It the spare has no problems then I guess it's the device. If they both do it's something in Windows. Try removing and selecting a new one from scratch.