Travelling via trains

Not the Eurail pass for sure.

If you book ahead there might be discounted deals between Florence and Milan since that is the only portion on high speed train between Lucca and Lake Como/Milan.
The rest of your travel is on very cheap Regional trains (commuter type trains)

Point to point. Some of the longer distance trains can be purchased in advance at a discount.
Compare all routes at Trenitalia and Italotren websites.

italotreno has a promotion for group travel, not sure if you can use it. I use their app as well as the website and have had an issue with the website recently, but could book through on the app.
As others have said, there's a pretty big discount for booking ahead but they're typically nonchangeable nonrefundable. Although read the fine print, for a small amount per ticket on some ticket classes you can get up to 80%back. It's probably not a good idea to try for non refundable discounted tickets on the day of your arrival, but if you know what days you'll be traveling between sites the savings are pretty amazing.

I used Italo trains in March 2023 to travel between Rome, Florence, Venice and back to Rome. The only issue I had was the rookie mistake of booking non refundable tickets to Florence on the day of arrival - in fact the price difference was so much I booked 2 sets figuring it was still cheaper by a lot than the full price. Of course our flight from Boston was cancelled and we didn't arrive until the next day, but we lucked out in that Aerlingus reimbursed up for the cost of the full price ticket (as well as the flights, hotels etc). But, from now on I'll either try to stay in the city we land in on the first night or pay full price.