Lake Lucerne: Full loop

This route involves a 2km 400m+ hike up with the bike on your shoulders.

4h40 minutes of moving time (I am not particularly fast)

To connect asphalt with asphalt from Bauen to Seelisberg you will have a 2km stony path with 400 metres of ascent where you will have to carry the bike (on your shoulder).
The path is categorised as "yellow" (easy walking trail). It is mostly stairs.

Assuming that you do the loop having the water to your right hand (the most advisable from views standpoint you will reach Bauen and you will have to dismount.

I was carrying an 8 kilo roadbike with 1litre of water and it was ok, alternating between one shoulder and the other. I use SPD mountain bike shoes with a softer rubber sole than most stiff "look" system road bike shoes. You can still walk up in those shoes but you are more likely to scratch/damage them (a pair of running shoes with thread might be useful as alternative).

An electric bike would be too heavy to carry uphill. A regular mountain bike is doable but again, it´s 400 metres of ascent with the bike on your shoulder..

In the opposite direction, a mountain bike with good suspension ridden by a mountain biker (who can handle well going down many steps) may be able to do it without dismounting (it is a walking path so prepare to yield to hikers).

If you carry paniers on any form of weight do not try to do it uphill. It will be tough enough downhill.

You will go through following towns.

Brunnen
Sisikon
Flüelen
Isletten
Bauen
Seelisberg
Beckenried
Buochs
Stans
Horw
Luzern
Meggen
Merlischachen
Küssnacht am Rigi
Weggis
Vitznau
Gersau

(if you wanted to add more climb you could go up to the Bürgenstock from Bouchs and descend into Stans).

NB: note that summer 2024 they have prohibited cycling from Brunnen to Sisikon (until sometime in October) and they are operating a van that will load your bike for 6km.