Hi Marco,
Welcome to the cruel world of luger shooting. It takes some effort to get many lugers back into shape after years of abuse, wear and neglect. As mentioned in the thread, most fixes are not that hard.
As your barrel has been relined to 7.65, there is a chance that the mainspring was not adapted to the 7.65's characteristics, so you may want to investigate that issue when the other checks don't present the right results.
As a consolation: I've fired all my lugers and found that some needed quite some work to get them going again. Mostly it's finding the right magazine, swapping out trigger plates (and levers), and replacing worn out springs (extractor, ejector, mainspring). One gun even needed breaking in firing, as it had been restored to new in box conditions and the tolerances were a bit too tight. Not bad for a 70-year old gun.
The amount of flak received from fellow shooters who were quick to judge the luger but had never actually fired one was unbelievable, but it changed to respect pretty quickly
