I didn't turn up anything by Googling, which makes me pessimistic. I saw some unofficial luggage storage spots (bars and cafed) while traveling in Italy last yesr, but word of those usually shows up if you Google.
Last year I really needed to store a suitcase and a small tote bag while I visited the Villa Lante outside Viterbo. There was a fair-sized 3-star hotel near the train station where I figured some English would be spoken. I walked in with a 5-euro note in my hand and asked whether they would hold my bag. Success! There are no guarantees, though. You have to be prepared to go back yo the train station with your luggage and buy an onward ticket.
I've used the same technique (but only offering one euro) when I day-trip to a small town, find the tourist office closed and need a map. Desk clerks always seem to take pity on a mapless tourist. One euro in their pockets for a free map is a pretty good deal for them, too.