There are cases where the lower bound to solve some problems (e.g. sorting) have been proved to be less than any known algorithm at the time.
If you prove that the lower bound for any NP-Complete problem is O(p) where p is a polynomial, then P=NP and you do not necessarily have the algorithm.
A bit more weakly, some algorithms are known but do not have any implementations. I believe this is the case for the algorithm from "Triangulating a Simple Polygon in Linear Time".