The proposed operation certainly appears to be in the nature of "for hire and reward" as the charity is the beneficiary of a financial consideration in exchange for a flight.
My thoughts exactly. There is also a strong implication that the pilot and aircraft is for hire, which would not be legal if he is flying under Part 91 as implied.
There is a clause in the US FAA regs. for PPLs & private Ops to conduct flights for charity, under a number of conditions, but this is not legal under NZ CAA and I assume CASA rules.
My personal advice: don't do the flight unless you have written authorisation from CASA. It would probably be better for all involved if you sponsored a flying lesson for the lottery winner with the nearest flying club.