PNG can be lossy. It can be done by first discarding some image detail, to make adjacent almost-matching pixel values actually match, to be more amenable to PNG's compression method. pngquant.org has a tool that does it.

There are usage cases where you might want lossy PNG over other formats; one is for still captures of 2d animated cartoon content, where H.264 tended to blur the sharp edges and flat color areas and this approach can compensate for that.