To check the timetable on Trenitalia look for next Sunday. Regional trains' schedules are loaded weekly for the next 7 days.
There are 2 train departures every hour that you can take until later that evening. The trip is ~4.5hours long in total.
Generally the trip requires 3 trains:
1-Fiumicino Aeroporto-Roma Termini - (Regional train)
2-Roma Termini-Firenze SMN (Florence) - (Freccia high speed train)
3-Firenze SMN-Lucca (Regional train)
A few options are via the coastal route (via Pisa) instead of via Florence.
If you can depart from Fiumicino station at 15:08, there is a Frecciargento to Venice that departs from the airport. That option saves you one train change at Roma Termini because it goes from the airport directly to Florence.
Check the options on Trenitalia for the next Sunday. If you want to buy ahead of time a discounted ticket for the Roma T. To Florence segment on the high speed train you can. However it's risky because you don't know if the plane will land on time or how long the passport control will take. Discounted tickets become null and void if you miss the specific train you book and are not refundable.