It's customary to have the receiving carrier handle it.

It makes sense in general as a matter of policy because 1) you often don't know where the mishandling occurred -- they're trying to locate the bag not assign blame; and 2) your originating carrier may not have facilities at the other end (they do in this case since it's FRA, but sometimes they might not if it were a different town), and/or they may not have access to remedies in the city or country of your final destination, whereas the delivering carrier is more equipped to provide assistance.

I'm not sure how it gets handled financially -- if LH proves it's CO's fault and bills it back to CO or if LH just eats it, but that's the way it works. Similarly if someone flies LH connecting to CO and LH misloads the bag, CO has to handle it on the CO side.

I'm surprised they didn't VDB people to get the weight down -- that's what typically happens since VDBs payout TCs (funny money) while interim expenses and replacement clothing cost real cash. And if they're going to mishandle bags, why deliberately mishandle Priority bags from a Star Gold travelling on an international interline connection? Now if LH has to eat these costs, the evil side of me wonders if CO deliberately held your bag(s) back because they knew it was interline and their liability would be nil.