Arrival in Lucca
From Pisa Airport (PSA), you can take a train to Lucca with change in Pisa Centrale station.
From Florence Airport (FLR), take a public bus to Florence Santa Maria Novella Train Station, and then a train to Lucca (with change in Pisa Centrale).
Departure from Siena
On departure, if flying from Pisa airport PSA, you first need to reach Florence by bus. Once in Florence, you need to take a train to Pisa Central Station. From there, you can reach the airport by either bus or train.
As an alternative, you can catch a bus from Siena station to Pisa aiport: www.tiemmespa.it.
You can also reach Pisa from Siena by train, but you always have to change in Empoli.
If flying from Florence airport FLR, you first need to reach Florence train station Santa Maria Novella by either bus or train (both direct). Once in Santa Maria Novella, you can reach the airport by either taxi or bus.