We are going to be docked in Livorno overnight Nov. 15-16/19. On the first day we have arranged a tour to Florence. On the second day is it practical to go to Pisa and Lucca on our own and be back to the ship in plenty of time for a 6 PM departure?
That is very well possible. There are at least two trains per hour from Livorno to Pisa, from Pisa to Lucca, and back from Lucca to Livorno. See the schedule and travelling times at the website of the Italian railways. The regional trains (indicated with an R) don't come with a reservation, so you can buy your tickets at the station before departure.
Thanks for your help.
One thing: don't forget to validate your tickets before boarding the train if you want to avoid a hefty fine. It is explained by the European train expert Man in Seat 61 (see section »Ticket validation...«)