What is wrong with LibGDX? It gives you the same control as LWJGL (glXX functions) but ports to more platforms (Android, iOS, HTML5), includes more utilities (vecmath, texture/audio decoding, GUI, shader/VBO utils, texture packing, freetype fonts, etc), and has a wider community for gamedev.
Anyways -- you don't need Slick2D for loading textures. In fact, I would recommend against it -- Slick2D/SlickUtil is old and buggy, and not based on "modern" OpenGL techniques.
If you want to write your own texture loader, see here:https://github.com/mattdesl/lwjgl-basics/wiki/Textures
But like I said; LibGDX is more powerful than LWJGL and usually a far wiser choice.