That's a bit of a 'stumper'! No experience and it is an unusual one.
According to CX website business pax cannot take a guest into the lounge, but as you are OWS then you should be able to, but perhaps only in OW lounges?
I've only flown CX out of AKL once (about 5 years ago) and QF was (logically) the designated lounge then. Perhaps because NZ have a recently renovated lounge and QF's are desperately in need of same, is the reason CX have switched?
Hopefully someone else with experience can assist, but if not, I guess you'll have to try it out and see (and let us know). I guess two of you in the old QF lounge is better than one of you in the new NZ lounge?