Yes unfortunately this is how rewards work. You will have to either reschedule to another flight with awards availability, or get a refund. Air NZ won't (and neither does it want to) re-book you onto a revenue fare class.

The only exception is if you are close to departure and the ticket control is handed over to LX. In that case LX can (and normally does) re-accomodate you onto another flight irrespective of award availability as if you are travelling on a revenue ticket.

Edit: What do you mean by schedule change? Is the flight number still the same? If so then that is weird as you should have still been booked onto that flight. If the "schedule change" resulted in a different flight then the above holds.