We recently had an experience where LH delayed baggage delivery (for more than a week at the destination) for my wife and 2 kids traveling in J and they completely destroyed one of the bags in the process. It took us 90+ days of getting the run around before they finally sent a check. Twitter and social media streams were of no help. Calling any of the associated phone numbers were a waste of time and email only produced results after the aforementioned time frame. That time was spent with numerous outright lies from various respondents in the email chain and after being confronted with evidence of their incompetence and written false claims a check finally arrived in the mail.
It's certainly not what I would have expected from an alleged 5* 1st world European airline/carrier that we all travel on regularly in premium cabins.....YMMV