Why not make use of the opportunity to have a nice Swiss travel experience?
Spend one night in Luzern, then the next day take the Treno Gottardo from Luzern to Locarno in Ticino, in the Italian-speaking area of Switzerland, for an overnight by the lake. You can spend the morning enjoying the town and the lake, and take an afternoon train for the 4-hour journey to Florence (with a single train change at MilanO.
https://www.mystsnet.com/en/download/image-treno-gottardo-with-the-church-of-wassen/?wpdmdl=30206&refresh=65e85d8bbb3d61709727115
Or there is the Gotthard Panorama Express, a journey by boat and train from Luzern to Lugano.
https://www.myswitzerland.com/en-us/experiences/gotthard-panorama-express/
This one is only once a day, and all in First Class, but you could duplicate it on the Treno Gottardo by taking a boat down the lake from Luzern to Flüelen and boarding the Treno Gottardo there. The boat and train are timed to facilitate that. We did this with our family in September and everyone loved the experience.
If you choose the route to Locarno, there are lakefront hotels just 2-3 blocks from the train station, such as this one:
https://www.hotelgeranio.ch/en/
I have noticed that hotels near the train station are harder to find in Lugano, which is one reason (of several) that I prefer the Treno Gottardo and Locarno over the Gotthard Panorama Express ending in Lugano. The boat ride and the train tracks are the same, and you have more flexibility in the schedule.
Look at these maps of the Swiss rail system and you will see that this is the most direct route between Luzern and MIlan, your gateway to the rest of Italy.
https://www.mystsnet.com/en/download/swiss-travel-system-map-en-2023/?wpdmdl=14294&masterkey=63a023c8da36c
It also has the benefit of being very scenic, especially if you use the boat option.