You need to change your second flight. If you don't, you face buying a new ticket on the day for five or six times the price.
Let us assume that, as you say, you have a two hour connection time. And let's assume that the first flight is on time.
Air NZ use gates at T1 which typically entail around a 15 minute walk to passport control, even if you are in Business Premier and disembark first.
At passport control you can reasonably forsee a 5 minute wait if you have an EU passport, or a 20 minute wait if you don't.
You will then take around 5 minutes to go to get a trolley and reclaim your luggage. Your bags may already be waiting (it's already 25 minutes since you landed), but I commonly end up waiting another 20 minutes. We are now at 45 minutes from the time your plane landed.
You then need to make your way to Heathrow Central tube station, which if you don't know the airport will take another 10 minutes. You then have a wait of 1-15 minutes for a Heathrow Express train to Terminal 5, and the train will take 3 minutes. (It is now around 65 minutes since you disembarked from NZ2).
You will then take another ten minutes at best to get to BA check-in. It's 75 minutes since you got off NZ2.
But here is the killer. BA require you to pass check-in a minimum of 45 minutes prior to departure. They require you to pass security a minimum of 35 minutes prior to departure. And they require you to be at the gate 20 minutes prior to departure, or you will be denied boarding.
In other words, your current itinerary can only work if the NZ flight is operating early, and if the NZ staff at LAX incorrectly allow your luggage to be checked through to CDG. And if you have an EU passport.
If any of those things don't eventuate, you will be buying a new ticket at LHR at grossly inflated prices.