Go to Pisa centrale (bus to Lucca where/how) or totally with train Roma termini to Lucca?
the fastest way is Via Florence (train change in Florence). No Pisa involved.
The fastest will be a Freccia train to Florence then a Regionale to Lucca. I didn't look it up, just an educated hunch.
Thanks.. What I thought but always willing to learn.
Check schedules here
www.trenitalia.com
Enter from Roma Termini to Lucca.
The Rome to Florence portion can be done aboard the www.italotreno.it