And even more fanart. I hope my human anatomy doesn't make your eyes bleed too badly.
There are actually spoilers in this, for whoever reads up on the light novel, "Earl and Fairy" by Mizue Tani.
Or its translations at least...

The light novel is the original concept, manga and anime are just based on it with a different storyline.
So...Yes, in the light novel, Lydia and Edgar eventually gets a kid named Alvin.