How long does it take to get through Florence airport?

Florence is a smaller airport, so very easy to navigate. At that time of night, I wouldn't expect it to be too busy, so getting your luggage to the carousel should be reasonably fast. I'd suggest taking a Taxi from the airport to Firenze SMN station (they have a flat rate, but I can't remember the exact amount). There are frequent departures to Lucca (some with one change).

First of all, since those trains are Regional trains, you don't need (and you shouldn't) buy them ahead of time.

Since you will arrive from (I presume) Frankfurt, you have already gone through passport control in Germany, therefore it will be like a domestic flight. FLR is a tiny regional airport and only a couple of flights per hour arrive there, so from touch down time to the time you are on the curb at the taxi stand it will be just a few minutes.

In any case, even if you miss that train, there is another one at 9:10pm and one at 10:10pm.

To save time I suggest that you ask the taxi to drop you off at the FIRENZE RIFREDI station, which is closer to the airport (10 min drive max) and all trains to Lucca stop there as well after departing from SMN.

But better yet, you could catch a bus directly in front of the airport, and be in Lucca even before the train. There is the last bus for Lucca departing from the airport at 7:25 pm (1925) and getting to Lucca 1h05min later.
I would try to catch that one first, and it doesn't work, head to the FIRENZE RIFREDI station with a taxi and catch the 8:10 pm (actually 8:16pm at RIFREDI) from there.

Bus schedule below:
http://www.lucca.cttnord.it/Linee_e_Orari/Linee_Extraurbane_(Validi_Fino_Al_14_Settembre)/L/461

Click on the Lucca-A11-Aeroporto di Peretola-Firenze and download the PDF timetable (Orario).

As said before Florence is a small airport, however, I was told security has been lately reinforced, so to make sure, I assume you are not an EU national, I would count on 45 min for eventual checks and take back your luggage. It takes around 20 minutes from airport to train station (25 euros+ 2euros per luggage). There is also the bus which takes you directly from airport to SMN station - really easy and cheap 5-6 euros/person.
Why don't you spend the night in Florence, have a nice dinner, watch night lit Ponte Vecchio and quietly take train to Lucca the next day morning? You will arrive Lucca and most restaurants will be close in Lucca.

The taxi flat fee from FLR to the city center is 22 euro + 1 euro per piece of baggage. There is a night and holiday supplement but it won't apply to you.
If you go to the Firenze Rifredi station, it will be less because it's closer.

It's a shame you just didn't fly into the much larger Pisa Airport. There are many budget airlines flying into there too. And it's very close to Lucca.

Thank you everyone for your assistance!