Yikes! That is annoying.
Luckily there are several good iFixit repair guides (right on this site) for the DS Lite.
When the top screen image shifts up and down the simplest thing to try is to open the bottom case - not the top case!
Find the brown ribbon cable coming from the top screen and follow the directions here on iFixit for gently flipping the connector latch and unplugging the cable.
Usually I use a clean pink pencil eraser and very, very lightly wipe the ribbon wire traces. Then reconnect, close the connector latch and try again.
If you still get the screen vibration you may have a creased or broken ribbon cable.
You will have to replace the entire top screen, because as far as I know, the cable is not available, nor is it easily replaceable.
This is actually not hard to do if you like tinkering and fixing things. The top screen can be found at places like dealextreme.com or eBay for $10-$15 USD including shipping.
Best of luck. Hope you are able to fix your DS Lite. I really love mine - though I only play old school GameBoy Advance games on it !