On Mt. Titlis I would suggest you take your time to play in the snow and to enjoy the sights. After the mountain you should spend some time at Engelberg. There is a wonderful easy walk along the river and back the other side of the valley.
Also Lucerne should not be visited in a rush. Go through the old town and over the medieval city wall, visit the open city towers and of course one or the other of the beautiful churches. On the way you will see Spreuer bridge and Kapell bridge. There is a map on www.luzern.com/en/sightseeing-fuehrungen click on the map and you will be able to see where the attractions are. Also a walk along the lake offers great views.