NZ won't take your booking via email. You will have to call them and get it all done over the phone. And they charge you a booking fee. You can easily avoid this by going to a travel agent. However these fares usually get ticketed in the first carrier's stock. In your case in TG stock. Or you can simply book on the official Star Alliance Book and Fly website below in which case you will be ticketed in LH stock.
staralliance.innosked.com