I honestly didn't know.
Does any of it interact with say the Image class in slick? I figure since slick is built on lwjgl it will work but...
When you're in eclipse and you select what to "import", just make sure you pick slick's Image library, and not LWJGL's. As far as using both Slick and
LWJGL's side by side in the same class, I'm honestly not sure how you'd go about that. (But I'm also not entirely sure why you'd want to.
(EDIT: Just realized I'm a dummy, LWJGL doesn't have an Image class in the first place, so this situation would never happen. My guess is the closest LWJGL equiv. is probably one of the "Texture" classes, but I'm unsure.)
Really though most of the stuff you'd want to access in LWJGL is probably the static getters/setters like GL11.glBlendFunc() and Display.getWidth()/Height(), Slick does a pretty decent job of wrapping everything else LWJGL does (for 2D games anyway).
I'd be careful though, because you may find yourself doing things directly in LWJGL that Slick can already handle, and while there's really nothing wrong with doing it, it may make your code really confusing if you have several classes mixing and matching LWJGL and Slick2d together. I really try to avoid using LWJGL directly as much as I can personally. I only go to LWGJL if I absolutely can't do it in slick2d, like my resizable window (while the game is running) that Slick doesn't support for some odd reason.
My advice would be to exhaust all options of doing it in Slick2d before you go to LWJGL, you'll be surprised to find out that Slick (as well as LibGDX) can handle a lot of very specific aspects of LWJGL. Of course, I guess the plus side is learning LWJGL instead is probably massively more beneficial than Slick2d or LibGDX in the long run. But most of what you'll be doing is LWJGL is just boilerplate stuff Slick/Lib do anyway.