There is also the bus option directly from the airport, which would be the fastest option if the bus schedule works for you.
The bus originates from downtown Florence (Piazza Vittorio Veneto near the Cascine Park), the bus stop at the airport is only an intermediate stop just before the bus enters the A11 freeway to Lucca. The bus is used by commuters a lot so there are multiple runs daily.
Timetable below (The bus line is 'DD') click under 'Orario', a PDF document.
https://lucca.cttnord.it/Linee_e_Orari/linee-extraurbane/L/573
In the PDF go to the second page (the first page is LUCCA-FLORENCE the second page is FLORENCE-LUCCA). The stop is called PERETOLA AEROPORTO.
The bus stop is a short walking distance from the terminal, on Viale Luder, the boulevard that leads to the A11 freeway. Here is the map location:
https://goo.gl/maps/SP6iFDpBy5QFVx8AA
Below is an image shot of the actual bus stop on viale Luder. The brown 3 story building in the background is the arrival terminal.
https://goo.gl/maps/DAnHuCptNZ62AfGa6