Can Collection.startIndex be implemented lazily?

I'm trying to implement a lazy collection wrapper. Figuring out where the first element is, if any, takes O(n). So I cached that location in a lazy stored property. The problem is that the implementation of the immutable startIndex can't call lazy properties! (They're automatically mutable, even if they're never reset after initialization.)

I guess I could do shenanigans with a class wrapper for the cache, but I wonder if there are better solutions. One question is if I need to do this at all; since this is going to be a wrapper accessed through LazyCollection, I could just force a recalculation every time startIndex is used. But that makes startIndex, and isEmpty and underestimatedCount, O(n) instead of O(1) every time. With my lazy idea, at least I could get amortized O(1) for all three.