i don't know if this is the good way to do it, but i did this effect once in a flash game, i made it like this :
-layer 1 = game (your 1st picture)
-layer 2 = a whole black square that cover the game with alpha value lower than 100%
-"layer" 3 = i said "layer" cause this one is related to the 2nd layer, it's a mask form that "delete" a certain area of the 2nd layer, so like that you'll have a light effect.
now i hope LWJGL expert will help you to realize these steps or give you a magic method to do it