Burton Frasher was a photographer, known for his "RPPC"...Real Photo Post Cards. I believe that the information you quoted is giving him credit for a photograph...not for creating "The Riding Lesson".

This is from an article that I wrote years ago...so I don't remember the source of the information:

In a flash of brilliance, the Town House hired a local commercial artist, Lew Hymers to design a logo for the club. The logo became the theme of the establishment, and the theme became the very essence of the club's being. The logo was a simple single line drawing of two women seated at a bar, on stools, between them is standing a lanky, bow legged cowboy. The drawing was entitled "the riding lesson." This simple drawing embodied humor, sex, recognition of the divorce industry's impact on Reno, and of course an inference of drinking, dining and gambling, all mainstays of the Town House' offerings. The logo was soon on virtually every piece of printed material pertaining to the club: matchbooks, postcards, stationery, business cards, etc. A large hand painted version of the "cartoon" was prominently displayed in the club. Racks of new H. C. Edwards (hub mold) chips were ordered with the drawing occupying one side of the chip.

John Moore did an article about Lew Hymers for the club magazine... https://ccgtcc-ccn.com/Lew%20Hymers.pdf

A couple of Frasher RPPCs (courtesy of the Pomona Public Library)