They cannot. Itineraries/PNRs cannot be merged.

What they *could* do is check the bag through....but they won't. Not so much for the reasons you wrote, but for many other reasons. (Interlining is a service intended only for single tickets, and airlines are increasingly distancing themselves from the practice of interlining across separate tickets, if only because it implicates them in the baggage retrieval/compensation process if the later airline on a completely different ticket loses it; and anyways, LH has long despised TK and does everything it can to deter its customers from straying to TK - look at the earning rates Miles & More offers on TK flights!!!)