Note that Airpoints membership is not the same as club membership (Red Carpet Club for example). If you're looking for lounge access you need to either be elite (generally *G with some exceptions) or be travelling business/first class.

*G on NZ Airpoints (or for that matter any *A FFP outside US) will provide access to the red carpet club when flying *A from or within us - a significant advantage over having status on UA Mileage Plus.