First off the why I think William G. Hogue may be Lewis Hogue's father: (btw: also believe it's Lewis J. not Lewis T.)
https://www.familysearch.org/ark:/61903/2:2:QFPY-KXF
https://www.familysearch.org/ark:/61903/2:2:3DNX-MRV
There is evidence my 2G-grandmother was Lewis Hogue's daughter
https://familysearch.org/ark:/61903/1:1:M8WM-55X
but as you see in these two similar genealogies, they refer to a "John Lewis Hogue" and a "Lewis John Hogue"
do you have anything else linking these two characters, and if you want to take it to that next step...who is (Caroline) Esther Hogue??