From the Melbourne Airport website:
Luggage Services

Says:
A luggage storage facility is available at Melbourne Airport through SmarteCarte.

Rates are per 24 hours per piece:
- Hand luggage $10
- Suitcase/Backpack/Golf bags $14
- Skis/Bicycles/surfboards $20

Located in T2 Arrivals, SmarteCarte operates from 5am to 12.30am, 7 days a week. Photo ID is required for storage. (If desk is unattended at any time, pick up phone located at the desk).

I think he'd have more fun in the city though!