There could be one or more of several problems.
If after cocking the Luger it fails to 'click' when you pull the trigger ON AN EMPTY CHAMBER, the first thing to check is to see if the safety is on (duh).
Since it is not very likely that this is the problem if it is YOUR Luger, then Lets begin to diagnose the problem.
Remove the slide by opening the toggles to full height with and EMPTY magazine in the pistol. The toggle should remain in the open position. Remove the magazine.
Turn the takedown lever to the 6 o'clock position and then release the toggle slowly to remove the slide.
Open and close the toggle. You should feel the resistance of the firing pin catching on the sear and compressing the firing pin spring when you close the last half inch or so of the toggle before it is locked closed.
If that is happening, then you should be able to drop the firing pin by depressing on the front of of the sear (trigger) bar (see diagram and press on the left end of the sear bar - part # 018).
If the firing pin drops, then the problem is in the trigger or sideplate. If it doesn't happen, then the problem in with the sear and firing pin engagement. One or the other of these parts may be worn or broken.
Do this test and post the results to this message and one of us will be able to advise you on what to do next to determine the problem.
Just a caution, Lugers should rarely be dry-fired. If you do this a lot, it will likely break some of the fire control components due to impact stress. You can make a safe 'snap-cap' for dry firing purposes using a deprimed empty case and some really hard rubber from a good pencil eraser or a tire that has been cut to fit in the primer home to catch the firing pin when it falls. The rubber should be periodically replaced when it has been beaten to the point where it no longer catches the firing pin with enough resistance to prevent breakage.
-John
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