And the answers are: Yes. Nothing.
Assuming that you mean that the flight is operated by LH, not just a codeshare, and is LH booking class Z.
Its an LH issued (220-) ticket for a flight operated by LH. Booked in LH Z. No problem. Keeping the account active is not a big hurdle either.
Can't wait to see the checking agents face when I ask to add my A-e-g-e-a-n Miles&Bonus number...