There is no installation for LWJGL really. Here's the steps to run an app using LWJGL:
1) Put lwjgl.jar in your project directory somewhere (I use /lib/). Right click your Eclipse project, Properties, Java Build Path, Libraries, Add JAR, add lwjgl.jar.
2) Click Run menu, Run Configurations, select Java Application, click tiny "new" button, type a name, pick your project and main class.
3) On the arguments tab, put "-Djava.library.path=/path/to/dir/containing/lwjgl".
On Windows, if you put the native libs (DLLs) in the root of your project (which is the default working directory when you run your app), then you don't need step 3.
I don't bother with the stupid user libraries.
Instead of setting the -Djava.library.path parameter you can also just drag the dll (or the file for whatever OS you're using) into the src folder in your project.
Only on Windows, and they have to be in the working directory defined on the Arguments tab, not in the src folder.