Oh, I figured it out.
This worked:
java -cp lib/lwjgl.jar;JVA_GameProject.jar -Djava.library.path="lib/natives" main.EngineLauncher
Classpath is for Java Classes (that much I had started to guess, if it wasn't immediately obvious) and java.library.path is for Native Libraries, it appears. The other problem I had had was that I was writing "lib/natives/lwjgl.dll" instead of just the directory; hence why eclipse always only asked for the directory...