I have a feeling this is a commonly asked question, how can I get Xbox 360 rumblers to work?
Short version: you can't, sorry. Blame Microsoft.
Long version: On windows there are two input APIs: the older DirectInput, and the newer XInput. DirectInput has been around for ages, and pretty much all controllers use it and are supported by it. It worked great, but it was a bit complicated due to supporting lots of different device capabilities (dpads, analog sticks, sliders, buttons, flight stick hats, vibration, etc.).
When the 360 came out, MS also released the XInput API. It's a simpler input api largely built around the 360 input devices, and works on Windows and 360, to make it easier to port games between the two. The 360 pad on windows can be used under each device, *but* to try and drive XInput use, the 360 pad is somewhat nerfed if you use DirectInput, and you can't use the rumble if you're talking to it via DirectInput (IIRC you also can't get all of the button states, and you can't talk to the center ring leds, or get the battery status). If you use XInput you get all functionality, but you can only talk to official 360 pads.
LWJGL only uses DirectInput, so you get nerfed 360 support. Which is a shame, but writing an entire back-end for one controller kinda sucks.