best day trip experience from Luzern to see mountains?

Take the Lake Steamer along the Lake to the south end and return.
Or, take the Gotthard Panorama Express Train the does the Lake voyage and then take the train over the mountains to Bellinzona in Ticino, and return to Luzern through the Gotthard tunnel.
https://www.sbb.ch/en/leisure-holidays/trains-boats/panorama-trains/gotthard-panorama-express.html

Go to Engelberg and Mt Titlis. It is IN the Alps. Engelberg is only 45 minutes from Luzern by hourly trains.
https://www.titlis.ch/en

I second Titlis!

You could also go to the Schilthorn or Jungfrau as a daytrip, if you REALLY want mountains. The former is usually preferred, and you'll get to ride the portion of the Golden Pass railway from Luzern to Interlaken.

I will “third” the vote for Titlis, which is every bit as much of a mountain as the Schilthorn or the Jungfrau (and actually there you are at a saddle between mountains). And a lot closer to Luzern. Also, at this time and for the foreseeable future, the Golden Pass train between Luzern and Interlaken Ost goes only as far as Meiringen. From there you ride a bus through a tunnel, missing the scenery along Lake Brienz. This is due to damaged tracks at Brienz caused by the recent flooding and rockslides.

I will fourth Titlis. We spent a few days in Lucerne in winter back in 2014, and did a day trip there.

To this day it is probably the most memorable day trip I have ever had, so much so that we are returning next month to visit more of Switzerland, this time the Matterhorn and the BO Region.

I have no doubt though that Titlis is a real mountain with real snow. It was an incredible day, and using a Tell Pass, not particularly expensive.

I don't know how to post photos on here, but if you message me I can send you some, they are really beautiful.

BTW, If you are going to Engelberg from Buergenstock Resort, the best way is a bus to Stansted, then a very short train ride to Stans, where you catch the train to Engelberg. www.sbb.ch/en says it takes 1 hour and 8 minutes.

Thanks, everyone!
Sam, that's a great idea - to go directly from Burgenstock to Titlis. That will save us a lot of time. I am guessing the train ride will be scenic too!

I went to Titlus in July. Seemed like less crowds than Pilatus. Take some time to visit Trubsee on the way down.