I did not read all the posts so perhaps someone else also had experience with bikes on Lufthansa. I flew from NYC to Edinburgh/ Copenhagen to NYC in 2015. Overall, great experience but not trouble free.
1. At NYC airport, the people at the desk were not well trained. We were prepared for this and insisted on a manager. She was not well versed. 20 minutes later, she returned to the counter, I assume after speaking to Lufthansa, understanding the roll on policy. They took our bikes at that point. (Mu understanding is that the airport ticket takers are outsourced and perhaps not trained as well. Especially for something like bikes on planes which does not happen often, I do not believe)
2. We were able to see our bikes at the layover airport from the window. They were in the airport runway moving carts. One had fallen. The other upright. We were concerned they would not make our flight since they were not loaded while we were getting on the plane. They arrived with us, however.
3. Only problem upon arrival in E was one of the bikes had a damaged fender. It was the bike that had fallen. Perhaps the fall was the caused or it was coincidental. We took pictures and replaced the fender at a LBS. We were refunded the entire amount.
4. From Copenhagen to NYC, bikes arrived with no damage
We have put our bikes on planes and shipped them UPS in the States over the years. Lufthansa was equal or better than those experience which were typically pretty good.
Let me know if you/others have questions.