Luzern [ Lucerne ] activities in December

...what we would do in Luzern if the early December weather is really cold/cloudy....

We were in Luzern the first few days of March three years ago. Luzern is at a low elevation which probably accounts for it being a population center in contrast to higher elevation mountainous locations. Life goes on in the late fall as it does winter in places like Luzern. You just have to dress for late fall/early winter conditions recognizing that daylight hours in December are shorter than September. The usual suggestion of dressing in layers and having gloves and a cap apply to December.

You can check the Luzern calendar of events website, setting the filter to the December period of you planned visit: https://www.luzern.com/en/highlights/calendar-of-events/

Clicking on the "filters" tab and selecting the December 2019 period and searching for traditional and festivals:
https://www.luzern.com/en/highlights/calendar-of-events/?tx_solr%5Bsent%5D=1&tx_solr%5Bfilter%5D%5B%5D=attribute_173%3A201912010000-201912310000&tx_solr%5Bfilter%5D%5B%5D=attribute_287%3A4885&tx_solr%5Bfilter%5D%5B%5D=attribute_287%3A4886
Results include two Christmas markets, an advent concert and a Christmas concert.

And if you want a more winter environment head for the hill such as the Davos-Klosters area that we visited: https://www.davos.ch/en/winter/activities/

I wouldn't go back there if you are questioning it. I was There a 2nd time last week; it was kind of ok meh what else is there to do. Similar to Bern it is over run with large bus tour groups (you know where the tour guide is carrying a flag leading the group) blocking the streets taking pictures oblivious to other traffic

Thanks for the in-depth replies . I appreciate your time!