I agree that LH has little market for such a large plane. In the event that they buy these birds, i see them being used on the following routes:

1: FRA-ORD / Already LH has one 747 and one A340 on this route daily. This route feeds into UA's domestic system well. I would invision them cutting the 747 and the A340 in favor of the A3XX once per day.

2: FRA-LAX or FRA-SFO
LH has 2 daily 744 flights to LAX, which proves that they must have enough pax for the A3XX, however, SFO fits better as a feeder for UA.

3: FRA-IAD. They already havean a340 and 744 on this route so the load and feed factors fit.

4: FRA-JFK....duh