Are lockers at the train stations safe?

Yes.

I've never heard a complaint about a loss from lockers or baggage check.

Rich,

I don't know about those 2 stations (never been to them) but on my travels the last few years the lockers in Italian train stations I've visited have been closed due to terrorism concerns. Instead they have staffed luggage check (Deposito Bagagli)where you get a tag and pay by the duration you leave the luggage.

(edit) Not all train stations have staffed luggage check. It tends to be at the larger stations.

Rich, Mike is correct. These two stations have staffed luggage storage areas. No more lockers due to security concerns. Below is one of my previous comments on the one at Pisa which we have personally used.

There is a tremendous staffed baggage storage place at the Pisa train station. We have used it. With your back to the station and your front to Track #1, turn left and go down almost to the end of the buildings. Turn left between the last two buildings and walk towards the building in the rear right. You will see a sign that says baggage storage in Italian (which I forget). The staff there will store your baggage behind the counter AND will ask for your passport to photocopy your picture. A piece of paper with your picture will be placed with your luggage. Then, when you return, you have to show your passport to get your luggage back. 3Euros per bag. Works great.

Thank you for the information. By being able to safely store our luggage, we can sightsee through Pisa on our way from Cinque Terre to Florence, rather than making a separate day trip back.