For the afternoon, I suggest visiting one of the mountain viewpoints near Lucerne city, either Mt Pilatus or Mt Rigi, which are both close to the city.
I slightly prefer Mt Rigi because, in winter, you can still take a boat to the base of Mt Rigi before riding to the peak on a cogwheel train. Also the trains run later in the afternoon, so you don't have to hurry so much to get back before the last train.
If you prefer more drama and a cable car ride, Mt Pilatus is a good choice for you.
If you are traveling on a Swiss Travel Pass, the entire journey to Mt Rigi is included with your pass. For Mt Pilatus, you get a discount.
In any case, check the timetables carefully to make sure you don't miss the last train or cable car down the mountain.
If you choose to visit Mt Rigi, you might a late afternoon visit to the mineral baths which have a warm infinity pool that overlooking Lake Lucerne and the mountains.
