It can be a bit difficult for new visitors to Italy to understand the parking signs.
In many places in Bagni di Lucca (and other places) you will see this sign.
It means you can park for free, but only for 2 hours, between the hours of 8.00am to 8.00pm. Outside these hours parking for longer periods is OK.
The little dial on the bottom left of the sign indicates that you need to set your timer.
In your car you should have a timer. Set this at the time you park your car and remember to come back before the time expires.
Your hire car should have one. If not, I have found them for a couple of euros at Tabacchi and some newsagents.
If you forget to set your timer that is no excuse. If the police come you will be issued with a fine.