Full auto?
First and obvious thing would be to tear it down, make sure it's clean and properly lubed, look for any obviously worn or broken parts, etc.
Past that, while I'm pretty familiar with how a Luger works properly, I don't claim to be any expert on what makes them go full auto. I would consider it a dangerous condition. If the striker drops before the action is fully locked the pistol can fire. Firing with out the action fully locked up doesn't bear thinking about.
I would take a very close look at the upper part of the trigger lever, the dis-connector, the sear, and the notch.
The trigger lever is the movable piece in the side plate after you take it off. The upper end should have a little ramp that lets the dis-connector slide forward when the trigger is released.
The dis-connector is the little spring loaded plunger in the front end of the sear bar. It should move freely.
The sear is on the other end of the sear bar and is seen inside the frame when torn down.
The notch is not really a notch in the Luger, but a flat surface on the front of an ear on the striker that protrudes through the left side of the block.
When the breech block returns to battery, the sear stops the striker from going all the way forward with the breech block, thus cocking the striker.
With the pistol assembled, and double checked to be sure it's empty, pull the toggle back and allow it to go forward very slowly. On the majority of Lugers the breech block will stop when the sear engages and not go all the way forward. Jiggle the action a bit and see if the striler will slip off the sear. If not, then at this point you can pull the trigger and check for a proper release. The trigger should be a military style two stage trigger with some slack take up and then stiffen before breaking. If the Luger is a poorly fitted mismatch the trigger may be creepy, but it should not do anything really funny.
Go to
http://www.lugerforum.com/ and ask there. (You will have to sign up.) That's where all the Luger gurus hang out. I'm sort of one of them, but going full auto is not my area of expertise. Luger Doc could probably give some advice.