If Lilly was her maiden name then she was probably the daughter of George Henderson (Hent) Lilly Sr. and Bertha Maywood Lilly.
Roxanna Alice Lilly is mentioned in the 1969 obituary of her mother as living in Chicago. She is also mentioned in the 1976 obituary of her father as living in Chicago, but by that time she had married and her last name was Barber.