Additional: I thought I should explain this a little more.
The problem you're hitting is that LWJGL's use of OpenGL has been designed for a very different purpose than that which Java2D was designed for. These differencies manifest themselves in a complete lack of interoperability!
However, the path between your Java2D app and GL4Java is quite easy, then when/if you've moved away from Java2D, the path to LWJGL becomes easy as well.
However, that's probably some time in the future. You may not even need the features of LWJGL over GL4Java.