"In Transit" at Auckland?

Hi,

We are flying LAX-AKL-SYD in a few weeks and have about 90 minutes from touchdown of our LAX-AKL flight, before our AKL-SYD flight leaves (so an hour till that plane boards). I would assume this is enough time to transit but wanted to get some advice.

Is there an "In Transit" lane at customs/immigration? Will we need to claim then recheck bags?

Would a US citizen take any different lane/path than a UK citizen (both are departing from the US and ending in Australia)?

We will be flying Air New Zealand in Business Class (so should be among the first off the plane which helps with the immigration lines), landing at 7:40 AM on a Tuesday and departing back out at 9:00.

Thanks in advance!