You should see the Lion Monument too.
Skip the Gletschergarten. its not that interesting, and if the weather is nice, you should enjoy a Walk on the city wall, and have a cup of coffee on one of the small squares in Luzern old town, and enjoy the nicely painted houses.
I have not been on a walk along the lake yet, but i am sure thats also an option as well as the boats.
Enjoy the day in Luzern
Doc.