Bernina Express

Then what is the most efficient way to get to Florence?

Second question first. Bernina Express drops you in Tirano, cross the Piazza to the Italian train station and take train to Milano Centrale station, then a highspeed train to Florence.

How do I get from Lucerne to Bernina Express?

Fastest way is train to Zurich (or Thalwil), then train to Chur.

If you want to do it one day, it will take 12 hours.

Use www.sbb.ch
Plan a trip from Luzern to Tirano via Chur.

This is going to be a long trip, so maybe break it up somewhere. Pontresina is a good half way point.