There are many bike rentals in Lucca, but there is one at the side of the piazza in front of the train station.
Yo can also leave your luggage here, 3 Euros for 3 hours and 5 for the day i think.
There is another bike rental and luggage storage inside the station on binario 1.
It could add up if you have multiple pieces of luggage, I suppose.
You might get a better bike inside the walls, including a tandem or a family pedal cart.