If your looking for a simple switch, then using LWJGL directly is not the best idea, it will mean you have to write lots of boiler plate code like game loop, etc.
a better choice would be to use
Slick2D. Its basically a thin library that sits on top of LWJGL and provides all the basics like, game loop, image loading, etc and it api is designed specifically to emulate that of Java2D so you should be able to move over your java2d project in no time. Plus if your going to do a 2d game you'll be reinventing the wheel and will probably end up writing code pretty similar to what Slick2D already provides.
Yea a lot of people have been telling me to do this, and I too think it is a good idea when I have a solid game idea that I want to crank out, but at the moment I just want to learn about it all and also I am just one who likes to do these on my own in a sense, something to me just feels odd about using other libraries that are suppose to make it easier to write games, its not so much the idea of "This is for noobs" because I know it is not, but I feel like I do not truly understand what is happening and why I am using certain things, i think.
LWJGL is notable for its lack of structure. Almost everything is static, so there's no need to pass anything around. There's one one display, so just make glWhatever calls however and wherever you like (within the same thread, naturally). Same goes for OpenAL, and the keyboard and mouse classes.
Whatever structure you build is up to you, LWJGL doesn't prescribe one.
Hmm, this actually clears up a lot, thanks!