PA101 From Germany, joined Jan 2005, 491 posts, RR: 1 Reply 1, posted (6 years 2 months 1 day 3 hours ago) and read 902 times:
You can ask the LH staff in Germany to tag your bags all the way through to SYD (show them the NZ ticket); should be no problem at all - however, you'll probably have to get your NZ boarding pass in LHR - NZ should have a desk a the FCC (Flight Connections Centre), through which you will have to pass, since you'll arrive in T2. Afterwards, you'll take the bus to T3.
If it's not too busy in LHR (usually, the morning hours are a nightmare), there should be no problem with making your connection.