I don't know if there's specific documentation on the XBOX360 controller with LWJGL, but if there is, I couldn't find it. However, perhaps you can try listing all the individual buttons. I don't have a controller, so I can't test this myself, but maybe:
for (int i = 0; i < controller.getButtonCount(); i++)
{
System.out.println("Button index " + i + " name: " + controller.getButtonName(i));
}
where "controller" is your Controller object for your 360 controller.