Equipment helps, but you also gotta know how to use it well.
With a DSLR, your advantages would be:
1) larger sensor allows you to preset a higher ISO speed and still get away with relatively much less sensor noise.
2) You have the option to mount a large external flash that gives you good lighting.
BUT in conclusion, if you keep going to iA mode on the LX3, means you don't really know how to maximize the capability of your camera. So if you get a DSLR and use its Auto mode.... ~shrug~ I can't guarantee if you'll see great improvement in your photos.