Under IATA rules (presume all carriers involved subscribe), it is your final carrier which bears the responsibility here and then recovers from others.

It sounds to me as though this was carrier #2 because you never flew carrier #3. Thus, you make your claim to carrier #2. If indeed it was carrier #3, you make your claim to #3 and they are in fact wrong.

Bear in mind that you will receive the value of the bag up the treaty maximum. The value is the fair market value of the bag today. Unless the bag was truly brand new and pristine and expensive, you are not likely to see much here.

As to the lock, forget it. Your bag was processed through at least two customs authorities. Don't know any authority which wouldn't simply cut & toss the lock. For what it's worth, locking a bad doesn't protect it in any way, shape or form and simply makes it a more likely target for theft by one of the myriad people who handle luggage.