Will there be problems if it hasn't been stamped in?
You can leave the EU, including Schengen, Ireland and the UK with just showing your New Zealand passport to the airline while checking in and leaving.
If you leave the Schengen area, you will pass through exist passport control. They might ask you about your missing entry stamp, so prepare for that.
If you still have your boarding cards from your flights to arrive in Europe, or can get copies from the mail or phone app, have them at hand.
If you have any proof you are an EU citizen, like an ID card, bring that. Also bring the police report that you have reported your passport lost.
Make sure you arrive at the airport early, as you may be asked to step in a separate room to be questioned.
I am not sure what is the best but I think I would approach the officer with 'I lost my (country name) passport but here is my NZ passport, which was not stamped as I handed the other one coming in.'