From Pisa airport:
Just outside the airport, take the people mover to Pisa Centrale train station. Regional trains to Lucca are frequent.
From Florence airport:
From the airport, take the tramway (T2 line) to Santa Maria Novella train station. Regional trains to Lucca are frequent.
From Bologna airport:
From the airport, take the shuttle to the central station and reach Florence by fast train (25-30 minutes). Once in Florence, take regional train to Lucca.