Although you could stay at the house without a car, we would recommend hiring one for independence and convenience, even though you may use it just to get from the airport to the house, and for trips to the station.
However, you can take the train from Pisa (usually changing at Lucca). Check the train times here to arrange your journey beforehand.
Please note that Bagni di Lucca station is actually in the neighbouring village of Fornoli, so not within walking distance of the house. Giuseppe Ridolfi (0583 805230) provides a very reliable taxi service.
Lazzi buses from Lucca take about 40 minutes. You can walk to the house from the bus station.