Lucerne Itinerary question

I think there is no need to fly Zurich to Venice. Train is as quick as 6.5 hours and that gets you all the way directly onto Venice Island. With plane you'll need to arrive 2 hours early into Zurich, do all the tedious security and waiting, possibly be delayed - then fly into Marco Polo and you'll STILL have to get from the airport to Venice Island. I would highly suggest train.

There's also a direct (no change) train from Zurich to Milano Centrale in as little as 3hrs 26 min.

If Bürgenstock still has the cliff walk that goes through a lovely wooded cliff above Lake Lucerne, be sure to enjoy that. It would be a nice easy and short activity while you're recovering from jet lag and sleep deprivation from your overseas flight on your first day.

On another day, allow at least 5 hours to explore the (car-free) Old Town part of medieval Luzern, allowing time to relax at cafes along the river Reuss, go up the ancient clock tower and walk along the ramparts, definitely cross the main wooden walking bridge full of flowers (Chapel Bridge). It's extremely charming. If you can't walk that much, you can take an open-air trolley tour through the town. Since you're staying at a nearby resort, you can probably make arrangements through the concierge. If not, The Luzern Tourist Information office can direct you (They give tours, too.) http://www.luzern.com/en/sightseeing-tours
And the Rick Steves Switzerland guide book is excellent, too.

You're actually on the outskirts of the Alps, not in the heart of it. You could drive to nearby Engelberg, and take the cable cars (gondolas) up to Mt. Titlis. https://www.titlis.ch/en
It has a year-round glacier up there. You can walk through a glacier tunnel with ice carvings, cross the cliff walk, then take the chairlift over the glacier to go sledding and snow tubing (in the summer). That's all I've done up there, but I see on their web site that they have hiking trails at lower levels of the mountain.