My experiences at LAX is that it is generally an efficient port and the Terminals are all fairly close together...so shouldn't be a drama getting to the other terminal for NZ.
The focus, of course, should be to get through Customs etc and get checked in for the NZ flight asap...then think about what to do with any time that's left over...if all goes smooth, I would 'guestimate' that you'd have about 1 to 1.5 hours left by the time you get to check in for the NZ flight...so, not too long really, as the flight will start boarding probably 45 mins or so before departure (I've taken 20 mins just to get off an arriving aircraft at LAX sometimes
...so time can easily get used up). C3PD