I also have a Henry Elmer Lyerla born April 05, 1891 in Tuscola Douglas County, Illinois. He married a Wavie. They had two children that I know of ...Mary and Rolla...these could be middle names or first names to your Henry and Mildred. Check the 1920 census Elmer Lyerla in Chicago and you'll see the names.
Henry Elmer's grandfather was from North Carolina and his father was born in Alto Pass, Union County, Illinois. I have additional information if you think we have a match
I did not quite understand your comment re Henry Elmer remarrying...Did Wavie die or ?