I found LX better than LH on long-haul flights, LH is pretty cramped in the back.
Another option for you is Thai Airways (TG) TLL-ARN-BKK-HKG, if you don't mind changing in BKK.
You do earn EB points in NZ economy, however not in the cheapest classes - but this is an issue with basically every *A carrier. Consult the EB website to make sure what booking class you need to get the full miles.