Transfer to Florence

There is a direct bus you can catch at Stazione Fs in Lucca that drops you off at FLR (1h): https://en.wikipedia.org/wiki/Stazione_FS_(Brescia_Metro). The first bus departs at 6:29a.

Honestly, if you need to be at the airport at 6:30 in the morning, I'd stay in Florence versus Lucca the night before. There is a train which leaves Lucca at 5:05 and arrives at SM Novella station at 6:38. From SM novella you'd need to take a cab (15 minutes, according to the airport website)) or tramway (20 minutes) to the airport.

https://www.aeroporto.firenze.it/en/the-passengers/transport/taxi.html
https://www.aeroporto.firenze.it/en/the-passengers/transport/tramway.html

I personally am risk-averse enough not to trust it all going like clockwork. What time is your flight, and does it have a connection somewhere else in Europe?

You could also use a private driver: much more expensive but an option.

The only way you can be at the airport by 6:30 in the morning is if you book a private car transfer (like a limo service) or a taxicab, because there are no public transportation options that can get you there that early. The earliest bus #DD (departing at 6:29am) can get you to the Guidoni T2 lightrail tramway (just one stop from the airport) is about 7:30am. The first train departs earlier (at about 5am) but it takes longer, so you'd get there no sooner than after 7, because the train arrives at 6:38 and then you need to walk to the taxi stand, get in line for the taxi and ride the taxi about 20 minutes (the T2 tramway takes also about 20 min).

The driving distance Lucca-FLR is about 50 miles, nearly entirely on the A11 freeway, and it takes almost one hour to drive it, assuming no traffic snarls (which at that time in the morning there should be none, unless there is an accident). The cost of a private transfer or taxi should be about 180€ for up to 3 people.

FWIW. We flew out of Peretola this fall and thought getting there at two hours ahead for our very early flight was overkill. When we got there the line to check in was over 100 people as all flights of our airline were being combined at one check in counter with 3 people. There were no facilities to just drop bags since we had boarding passes already. It was the worst check in experience we have had in years.

I'd stay in Florence the last night and get a very early cab to the airport and get there at least 90 minutes ahead of your flight. There is no way to get there from Lucca at that hour except by a very expensive car service ordered well in advance.

Thank you all for your help!

I’ve flown out of Florence many times and agree with janettravels, above.
The agents trickle in one by one, getting coffee, fixing their hair, exchanging gossip…. :o
It takes ages to get through the check-in desks, but somehow all the people always get through and to their planes on time.
Get there a bit earlier than two hours.
I would stay in Florence the night before.
Taxis to the airport are quick…20 minutes or less in the early morning.