I'll be posting up a Post Processing guide soon and Red Eye Reduction will be included in it. Suffice to say there's lots of different options and software to remove those red eyes out there!
Red Eye happens when the eye isn't prepared for the flash, so the iris is still open (usually in a dark environment). The Red Eye you see is actually the retina you can see because the iris is open. If you make sure that your focus assist light is turned on (I think more than just lumia's have this option?) you will not only prepare the eyes of your subjects because they'll get a flash before the picture is taken and you'll get a sharper picture, too!