Lucerne to Florence

The most direct train routes cross the border at Chiasso (but you don't get off there). You can buy a reserved ticket from that point at any Swiss train station. You'll change trains at Milan, so if you want to pre-purchase a reserved, advance-discount ticket from Milano to Florence, you can do that at www.trenitalia.com. Trenitalia may also sell a ticket from Chiasso, but if purchasing on that site, then be certain that it's offering you "ticketless" or print at home, rather than any ticket that requires picking up in an Italian train station. Most discounted tickets cannot be changed or refunded.

If you are travelling direct from Luzern to Florence, the quickest route (which is the route train websites will give you) is: Luzern - Arth-Goldau - (Gotthard Tunnel) - Lugano - Chiasso - Milan - Florence. Chiasso is the last Swiss station and the last place your Swiss Pass will be valid.
You can see all this on the official Swiss Pass map here: https://www.sbb.ch/content/dam/infrastruktur/trafimage/karten/karte-sts-pass-gueltigkeit.pdf

You therefore need to buy a ticket from Chiasso to Florence.
This ticket will be for a specific train, and have date, train ID and seat numbers on it. This ticket will be a lot cheaper if you buy it in advance on the internet. You can do this at the Italian Railways site: http://www.trenitalia.com/tcom-en
You will not need to get off the train at Chiasso, you can get on it earlier in Switzerland (Luzern or Arth-Goldau), and already be sitting in your assigned seat when you reach Chiasso