Congratulations on the speedy connection to the family. If you are interested in swapping information send me an email robertzingo at aol.com please. I will reply with a PDF chart of your ancestors and we can go from there if you want to make additions/corrections.
I am a 6 way Lilly descendant and Lilly researcher. If you are interested the Lilly Reunion group is also on Facebook under Lilly Family Reunion.
Similarly, if you are interested in doing some research I can recommend the Mormon site familysearch.org. No preaching, no obligation, nothing but lots of information. Hit the SEARCH button at the center top of the screen and then have fun. In a couple minutes time I found census information on your line and the WWI Draft Registration Card for Basil Green Adkins. A photo of the card is available, free, on the site.
