I believe that Harry and Lilly Dills could possibly be the children of Edward Dills (b. 1859 IL) and Cora Estelle Lewis (b. 1862 KS). Cora and Edward had other children as well, namely Lewis Dills (b. Unknown), May Dills (b. 1887 MO) and Ethel Estelle Dills (b. 1891, MO).
Apparently, after Cora and Edward died, Harry and Lilly went to live with Edgar Lewis and his wife in St. Louis. May and Ethel went to live with their grandfather, Alonzo Lewis, in Carthage. The only thing I know about Lewis Dills was that he was living in St. Louis in 1923, but I've been unable to locate him in any census or public record.
Lilly eventually married a brother of Edgar's and her last name then became "Lewis" which was, of course, her mother Cora's maiden name. I haven't found any information to indicate that Edgar Lewis and Cora Lewis were related and it was just a coincidence that they had the same last name.. confusing to be sure. My email address is crlilley@comcast.net, if you email me, I'll provide you with other info I have on these children and perhaps we can sort this out.
I also just posted some of this info on my tree at this ancestry web site, so you might want to take a look at that as well. Hope this helps and I hope we can work together!