Hi,
You are correct. There is no Green Lane at Auckland for embarkation. With regards to your status and priority boarding, when you go to Auckland, you will need to queue up with the lower classes 😛 for the immigration lines, but once through there, they then funnel you into more queues to have your paperwork checked, and receive your medallion etc. This is where you will be able to laud it over the rest, and go down a different lane which will, effectively, bring you out at the front of the main queue, to have your paperwork checked and medallion issued, then you can get straight on.