Fly into Pisa International Airport (PSA) — the most convenient option, just 20–30 minutes from Lucca.
Flights are available from most London airports, with Gatwick typically being the easiest.
Florence Airport (FLR) is another option, about 1 hour 10 minutes from Lucca by car or train.
From either airport:
You can take a taxi, hire a car, or catch a train to Lucca (direct trains from Pisa Centrale).