IanFromHKG

Oneworld FF access is for oneworld marketed and operated flights. Since NZ isn't oneworld, and assuming you have a NZ code on the ticket, you don't meet the criterion, unfortunately, nor will you benefit from the specIal arrangements with NZ ("Customers will also enjoy expanded opportunities to earn and redeem frequent flyer points or miles. Top-tier members from Air New Zealand’s Airpoints™ and Cathay Pacific’s The Marco Polo Club will enjoy reciprocal benefits when travelling on code-share flights, including lounge access, extra baggage allowances and many other priority services") since those don't extend to top-tier members of other oneworld airlines, only top-tier members with CX or NZ

Do you have a NZ or CX code on the ticket? If it is a CX code, then check in at the CX counters and you will probably get a lounge invitation anyway. But, as I said, with a NZ code you are probably out of luck