storing luggage at a train station

Yes you can. Not sure if same is true at all stations but info for other larger Italian stations is available at the link below. A quick google for the station you need will usually result in an info page about the station.

Venezia Santa Lucia - Left Luggage
On the ground floor, platform 1.
Opening Hours
7/7 days

06.00 - 23.00
Charges
6,00 € the first 5 hours
0,90 € /hour from 6th to 12th hour
0,40 € /hour from 13th hour on

One thing to watch out for: there is often a line to check bags and to retrieve them. You have to allow for extra time when retrieving a bag, or else you can miss your train.

Not all train stations have a place for left luggage (deposito baggagli). The larger ones do, but many of the smaller stations do not. It seems to depend on the level of staffing available. Orvieto, for example, has a small but busy station with no left luggage option, but there is a hotel somewhere nearby that will store luggage (it's mentioned in the RS Italy book).

The bahn.de website will show what services are available at nearly any train station in Europe.

Rick's intro to each town covered in his guidebook will have a summary of services under "Arrival: By Train." The description occasionally may not address bag storage, but usually does. It is certainly available at big-city main stations.

Thank you all so very much. it solves my problem.