Other than Jungfraujoch, which mountain day trip from Lucerne would offer the most "classic" view of snow covered mountains? I have been to the Rockys and I will never forget them. Its time for a new memory.
Near Lucerne, there is Mt. Pilatus.
We liked our excursion to the top of Mt. Rigi. We took a boat across the lake from Lucerne, then a cogwheel train up to the top.
If you want to see for yourself what kind of views you will get, take a look at the live webcams.
To scroll through all in the Luzern area, you can look here. There is also a map to show you the location of each webcam
https://www.luzern.com/en/information/planning/weather-webcams
If you just want to focus on individual mountains, look at the website for that mountain. Here is the one for Titlis
https://www.titlis.ch/en/webcams
Keep coming back because weather plays a big part in what you will see (or not see). I would do the same thing again just before heading out on your day of travel, choosing the local mountain that might provide you with the best view that day.
Our first Swiss mountain was Mt. Titlis, which we did on a day trip from Lucerne around ten years ago.
I have never forgotten it. It was winter, but we had a specactular clear day and it was completely wonderful.
We were back in Switzerland last week and saw other mountains, but none compare to that first time at Titlis. We didn't bother with Jungraujoch as it seemed to have the same attractions as Titlis did, but with many more crowds.