I have been unable to find any info on the Lily White Circle but I can answer your question about the "R G F".It is actually "R C F" which stands for Royal Circle of Friends.
"The Supreme Royal Circle of Friends of the World, also known as the Royal Circle of Friends (RCF), was an African-American fraternal organization founded in 1909 in Helena (Phillips County)(Ark). The organization was founded to supply insurance to the African-American population but was also dedicated to the moral, physical, social, and economic welfare of its members. Men and women were equal members."
This is the link to the webpage where I found this info.There is more to read on the subject there.