Ciao Brian,

Unfortunately, the Trenitalia website has this quirk - it shows no travel solutions at all for X time into the future...... it used to be 2 months but since we are less than 2 months from June 15th, I am not sure why it doesn't show any results!! Argh <hands in hair> is my usual reply to these types of situations --- they make no sense!

As Florence - Lucca is a regional train, you do NOT need to buy tickets ahead of time. Just consult the schedule online for any Sunday - like next week. You'll see the times. They are pretty much every hour. You can definitely do Florence - Lucca - Pisa - Florence all by train on a Sunday. I just don't know why that site works as it does most of the time. (Like I can't link to results on their site here on my reply because they just don't work!)