It probably won't work. Check in at LHR will only be as far as LAX. Transit in LAX is 2 hours, if the flight arrives on time. You'd need to clear immigration, collect any checked bags, clear customs, check in for the onward flight, and then through security. Bear in mind that immigration can take an hour on bad days (NZ tells *G passengers not in business to not go through immigration to the lounge).

Now NZ1 connecting to NZ5 has 2:45 connection, which is a bit more plausible although still somewhat risky (if flight from London is running late you could misconnect).