We rent cars in Italy because my husband's family lives in Tuscany off transit, and he's been driving in Italy since he was a teenager. I think we've ended up with a ticket in the mail months later almost every trip. We try our best, but it does seem to happen and we realize it's part of the deal so pay them when they eventually arrive.
I'm posting about this because we just got a ticket from early May 2023 . . . 20 months later.
Yes, we paid it. (My husband is from Lucca and we will travel there until we can't.) . . but do be careful of the dates when you get these tickets. In 2017 he had a rental car in Lucca Dec 26 - 31, and 9 months later he got a ticket. But when he looked at it closer, it was for November 2017 when he was definitely at home in Canada. No doubt he did something wrong while driving in Italy (we always do), but he didn't have to pay.
Also, the tickets are in Italian. But translation is easy now.
BTW - This time, we missed a flight and arrived very late at night in Pisa, so followed the GPS to our hotel within the walls of Lucca, and it was like that episode of Top Gear when they have to try to drive out of Lucca. The whole time we were saying "we are DEFINITELY getting a ticket!" GPS doesn't help you around these areas. Anyway, it was a fun adventure squeezing our tiny car into alleyways that I thought only a bicycle could get through. We don't actually know this was the event (you never do know), but seems clear.