So, simple question.
If i want to trigger something by clicking on a button, is there a way in which LWJGL can help me by knowing if I clicked on a certain texture OR do I have to do all the math checking clicking events and checking the mouse coordinates to see if it actually is on top of an image?

you need to do everything yourself, LWJGL is light (its in the name . To get what you want you want an engine of sorts, Libgdx and JMonkeyEngine are two engines that I beleive work with LWJGL.