We did airbnb in Lauterbrunnen last September and had a great experience.In 2008, we rented an apartment that is now listed on Airbnb and had a great experience. These are the two I have personally used, but I wouldn't limit myself to them. I would read reviews to know the ins and outs and pick the one that looked best to me:
We were with another couple in 2008 so needed 2 bedrooms. The place in 2018 had a 4 night minimun. I have a friend who picked this place because they were only staying 3 nights:
They were suppose to be 2 couples, but their friends canceled. Still she got it for $126 a night and that is good for the area. She will be staying there this September, so can't give you a personal reference yet. I think anything around $120 is a good price for this area. (In Germany and Austria, we were able to stay under $100 a night, but not Switzerland. I had to search hard to stay under $125.)
All these places have free car parking. We had a car too (picked up and dropped off in Germany, so...we had it and weren't getting rid of it loll) If you have a car, Lauterbrunnen is a great place to stay as many places provide parking. (But always check). If you stay up in Murren or Wengen, you have to pay to park your car in the public lot. Staying in Lauterbrunnen is our personal preference (easy access to the other towns and Innsbruck, etc) so it works great for us.