Marcy

If you are arriving on Lufthansa (Terminal 2) then you should be ok with luggage transferring to Terminal 3 for NZ as this hasn't been affected. If you are arriving on BA from Frankfurt (Terminal 5) then apparently things are ok, but there remains a risk while the backlog is getting cleared up. The Terminal 5 to Terminal 3 transfer will be far lengthier than Terminal 2 to Terminal 3, as Terminal 5 is not adjacent.

At Terminal 3 flying NZ in C you can use the United lounge, SAS/Air Canada "London Lounge" or the Singapore Airlines lounge. Of those I'd rank the United lounge as last, although it is the "official" lounge NZ uses, in that it is the only one with an NZ contracted staff rep on the counter and with announcements for the NZ flights. The SAS/Air Canada "London lounge" is roomy and pleasant, but the Singapore lounge is also nice and has better food. The Singapore one is slightly the "wrong" direction to the gates, but that only adds about 2 minutes compared to the SAS/Air Canada lounge.

All the best, hope you have good flights and a not too stressful experience at Heathrow.