<<"On the way to Zurich from Lauterbrunnen, we plan to spend about 10 hours in Lucerne. Can you suggest how we should plan our stay to maximize the benefit, given the duration?">>
it is tough to try to fit a week's worth of sightseeing into 10 hours. ;-)
This thread has some thoughts:
Anjan has given enough details to give a feeling for the possibilities, along with some good photos:
Lake Lucerne stands out as one feature that is is special about Lucerne.
By the way, I tend to use the German spelling, Luzern, pronounced the same way, because the Canton of Luzern is in the German-speaking part of Switzerland. The lakes bracketing Interlaken are quite nice, too, but Lake Luzern ( der Vierwaldstättersee, the Lake of the Four Forest Cantons) is larger and has a wide range of scenic possibilities. I like the southernmost part of the lake best, but it would take a significant part of your limited time to really get a good look at it.
Toward the end of this link, there are some photos that show the surroundings. I'd not recommend the walk that I describe there, because it would take too much of your time, but you'll get a hint of the possibilities for your next trip:
You might consider a boat ride as far as Alpnachstad, and the cograil up to the top of Pilatus. On a clear day, or even a cloudy one such as Anjan photographed, the views are quite nice, and it is close to Luzern.
This link shows all the boat schedules on the lake:
In the footnotes, there is a link to a map.
You could perhaps put together a short trip, to the Transport Museum ( das Verkehrshaus.) . Even that short trip would be nice.
The train to Alpnachstad is faster than the boat.
This map, if you turn on in the menus "Traffic" under Points of Interests, and select the type of transportation, can turn on an overlay with all the public transport stops.
map.search.ch/?pos=666928,210992&z=32 &poi=bergbahn,halteste lle,zug
Zoom in and click on any icon.
You could consider the one hour boat ride to Vitznau and the cograil to the top of the Rigi (Rigi Kulm.) but, once again,the total trip would consume a big part of your day. The Rigi has nice walks on it, and lots of open space and meadows, in contrast to Pilatus, so that some walks could be done, with more time required.
But, a boat ride to Vitznau and on to Brunnen has some chance of showing a large part of the lake, reaching the beginnings of the southern part (called der Urnersee) and getting you back to Luzern fairly quickly by train from Brunnen. The train station is a ten to fifteen minute walk from the boat pier in Brunnen, and you would need to look at at schedules for the train from Brunnnen with some care to see if that makes sense for you.
I would try hard to include a walk around Luzern . It is a small town. Aalk alog the river is obligatory, to see the Kapellbrücle (Chapel Bridge.)
I'd make sure to visit the Lion of Luzern, and, nearby, one of my favorite places is the Bourbaki panorama. All my friends and relatives from age 8 to senior citizens have enjoyed it:
The old town on the north bank of the Reuss River deserves a walk around. Lots of tourists, but the oldest part, along the river, should be explored a bit from in the town, not just the river walk alone.
This is a good place for a meal with nice views outdoors if the weather is nice, a varied menu, and good food quality, including vegetarian options:
translate.google.com/t ranslate?hl=en&sl=de&u=http://w ww.braui-luzern.ch/&prev=search
Walk up the steps on either side and into the old town
A walk along the lake shore through the gardens, from the Transport Museum to the Schwanenplatz (Place of the Swans) near the main bridge is about 1 and 1/2 kilometers, and is a good way to stretch your legs. You can see it on the map I linked above.
I've attached a few photos.