Rome to Lucca by train

Has anyone taken the train to Florence or Pisa, and then the Regional to Lucca?
Yes. Millions of people have every year.

Is there a coastal route?
Yes. Via Grosseto-Pisa.

Has anyone flown back to the States with a flight originating from Pisa?
Yes. Millions have over the years. Many are even today. Unfortunately Delta discontinued the Pisa - JFK non stop flight last year, so now the only option is to connect via some other European hub. Pisa has flights to Paris, Munich, Amsterdam, Rome, among others.

I guess I should have been more specific. What is the most efficient train route (time-wise) from Rome to Lucca? And is there a scenic coastal train route? Should tickets be purchased in advance for any leg of the trip?
Thanks

3hr 50min via the coastal route and a change in Pisa.

IC 510
Dep 09:57 ROMA TERMINI (Italy)
Arr 12:59 PISA CENTRALE (Italy)

RE 6765
Dep 13:20 PISA CENTRALE (Italy)
Arr 13:47 LUCCA (Italy)

Timing via Florence from 3hr 09min.

I don't know what is meant by most efficient, but the fastest is via Florence since the Rome to Florence line is a high speed railway line, while the coastal route via Grosseto and Pisa is not.

The coastal route is not particularly scenic as the railway is not exactly on the shore but at least a couple of miles away on the interior therefore you hardly see any sea water. The only exception is the few miles between Castiglioncello and Livorno, and a couple more spots at Santa Marinella and Civitavecchia, where the railway is indeed close enough to the sea.

For train timetables consult
www.trenitalia.com
Enter station names:
Roma Termini
Lucca

Tickets do not need to be purchased in advance, they can be purchased as late as few minutes before boarding the trains at the station. However purchasing in advance gives the possibility of obtaining discounted fares, which tend to sell out quickly. One warning however. Once you purchase a ticket at a discounted fare (supereconomy or economy fare) no changes or refunds are allowed, therefore you must be sure about your travel plans.

Roberto: Thanks for the link to the train website, and for the info about the coastal route.

David: Thanks also for the info of the coastal train route to Pisa. At Pisa it may be more advantageous to take the bus, but will need to research it more.
Carol