Apartments and holiday homes
If you stay for a week or longer, an apartment might be a good alternative to a hotel room. The supermarket in Lauterbrunnen allows you to get your groceries and cook your own meals. There are a few restaurants too.
The landlord or rental company will provide a free Guest Card upon arrival. The card provides various discounts on local attractions. Note that if you own a rail pass, you will get a better discount on many attractions.
Interhome offers thousands of holiday homes and apartments across Switzerland. They offer discounts on both early and last minute bookings. That makes the Interhome website a good place to start your search:
https://www.interhome.com/switzerland/: all holiday homes
https://www.interhome.com/switzerland/early-booking-discount/: find the discounts for early bookings
https://www.interhome.com/switzerland/last-minute/: find the last minute offers