The reason why Strata and Air NZ lounges are listed is that at least one OW airline uses either of them. CX has a JV with NZ on the AKL-HKG route and as a result CX flyers can use the Air NZ lounge, hence the listing. And as many have pointed out, all OW airlines use Strata right now hence Strata is also listed.

NZ and FJ only has a basic codeshare agreement, and that is for the NAN-LAX route operated by FJ. NZ and FJ compete on the AKL-NAN route and FJ flyers could never access the Air NZ lounge in AKL.