well, fwiw, I think you should contact minecraft support for this. There is nothing saying that there is a general issue with visible cursor in lwjgl in general.
IIRC Minecraft doesn't use LWJGL's mouse grab calls but instead rolls its own version using AWT.
I have tested this now with LWJGL 2.8.1 and all is working fine. Even if I force a heavy load of my system with other tasks the problem doesn't appear. On clicking "Back to game" I can see how the mouse cursor is removing and after ~1 second (because of the heavy load) the menu is closing. This could be an indication that this is an issue with LWJGL 2.8.3.
Remember this as there use to be a mouse grab bug on windows
with LWJGL 2.4 (which Minecraft still uses!). The bug has long since been fixed and Notch still owes spasi a beer for fixing it
Interesting that the version is so old (how can I figure it out?). I remember some months ago I was using the distributed version of LWJGL with Minecraft for ~1 year and had an annoying bug. On clicking in the game the window lost for a really short time the focus and the mouse cursor was visible. If an already pressed key was released in this time it get locked. My character in Minecraft was so running often automatically into the death.
I'm curious why you replaced the LWJGL that comes with Minecraft with a different version? And, for that matter, why you expect there to be no problems.
The outdated version of LWJGL distributed with Minecraft has more annoying bugs (see above or my linked thread). Using a newer version was much more comfortable. This allows me even to report bugs that I can find in LWJGL.