This is where we stayed as a family of 5 during our time in Lucerne. It's within walking distance of the train station, or you can take the bus. Bonus - they have air conditioning which is hard to find! They were able to fit all 5 of us in one room by adding a rollaway bed.
You can check availability and current prices here.
It's a great-value option if you want to stay close to Lucerne’s Old Town without paying lakefront hotel prices. This family-owned hotel sits in the quieter Bruch neighbourhood, but you can still walk to the river, Chapel Bridge, restaurants and Lucerne train station