Following is the link to the convenient front office of the Trenitalia website.
You can find out the train schedule, buy tickets online.
To get to Lucca from Florence or any other direction.
To get to Castelnuovo di Garfagnana from Lucca or Aulla.
From Lucca along the Serchio river you will cross the numerous villages of the Middle Serchio Valley, including Bagni di Lucca, Borgo a Mozzano, Barga - Gallicano, Castelnuovo di Garfagnana and then again towards Piazza Al Serchio, from where, if necessary, continue up to important Italian railway hub of Aulla.