Well, lessons != assets. I would say that if the founders create a new entity, and use assets from the old company in the new one, that it's reasonable for investors to claim a stake in the transferred assets/IP.

A good example of what usually happens with pivots is the case of Firebase (http://firebase.com). They used to be Envolve (https://www.envolve.com), but they saw demand for what they're doing now, and took the real-time technology behind Envolve to power Firebase.

I don't know if they kept the old company or set up a new one, but YC still has their stake in them.