It used to be possible at the train station but this is no longer possible.
Left luggage lockers are called CONSIGNA in Spanish
It is possible to leave bags and luggage in the left-luggage lockers at the Bus Station. For information about how to get to the bus station,
see
http://granadamap.com/airport/bus_stops.htmThe price is about 3.5 euros.
Click on the bus station balloon.
Buses 3 and 33 buses go to/from the bus station and stop on the Gran Via and Avenida de la Constitución
Also there are lockers at the Alhambra. It is free if you have bought a ticket.
The luggage office is located outside and downstairs from the main ticket office..