Can LWJGL support multiple displays either as separated windows or as part of an AWT Window?
From a bug report about multiple displays in LWJGL:
Do keep in mind that LWJGL 3.0 is at a pre-alpha stage and all APIs may be subject to change.
Closing this issue as there's no plan to implement multiple Displays in LWJGL 2.x.
So, if you're using version 2.x, no, LWJGL cannot support multiple displays. While it looks like there might be plans to do so in the future, I wouldn't plan on it for your own game, and I wouldn't start using the alpha for your development either.