Train from Rome to Florence and return from Lucca to Rome

Do I need to make a reservation ahead of time or can we wing it once we have landed?

You should buy it in advance only once you are certain that you are arriving on time to catch it. For example if your flight is guaranteed to arrive at 9am give your self at least 3 hours to get off the plane, walk to passport control, then to baggage claim and then to catch a train from FCO to Rome Termini station to catch a train to Florence. Otherwise wing it, but there are usually a couple of trains from FCO that go all the way to Firenze (Florence); it all depends on what time your flight arrives.

What is the easiest method of returning to Rome from Lucca?

Take the train with the least amount of connections and quickest travel times.
You would search from: Lucca To: Roma ( Tutte Le Stazioni ) and buy a ticket for that on this website:
https://www.trenitalia.com/en.html

The fastest routing from Lucca to Rome Termini takes 3:08 and involves a change of trains in Pisa.

The fast train tickets - Rome to Florence - can be booked ahead of time at some pretty serious discounts trading flexibility for lower prices. Coming back this is pretty straightforward because you can decide when you want to return to Rome ahead of time, but as mentioned predicting the timing after you land is more of a guess. You can buy "base" tickets which allow changes but there is little advantage between buying a base ticket ahead of time versus "winging it" and buying your tickets on the way to Rome when you're sure of your timing.

Trenitalia has an app that allows you to buy tickets and track trains that you should use.

The tickets for local connections like Lucca and Florence are local regionale trains and do not need to be booked ahead of time.

Have a great trip,
=Tod

We recently took the direct train at 13:53 from FCO to Florence, with multiple stops but no change. It worked out quite nicely for us - our flight arrived 30 mins earlier than the scheduled arrival time of 12pm. We got through passport control and to the platform within 30 mins upon arrival. We bought the train tickets in advance, business class, for under 20 euros each but we were ok with losing this money if there was a delay with our flight etc. Sounds like you'll be arriving in plenty of time to catch the same train.

Thank you all so much for the info. This helps alot!