Below is a copy of the driver’s license of my Great Grandfather, Francis (Frank) P. Lewis.
He would have obtained his in the very early days after they started to issue them, February 26, 1936 with it becoming a requirement on April 1, 1936.
I guess he couldn’t fathom paying a $200 fine for not having it.
A Younger Frank Lewis 
Below Is An Older Frank P. Lewis just prior to his passing in 1956.
This is a copy of a DL of my Grandfather, Andrew Theron Lewis.
He died in 1958.
This is a copy of a DL of my Father, Cecil Carroll Lewis.
History of Texas Drivers License
From the mid-1920s through the early ’30s, the issue came up whenever the Texas legislature met but was never passed.
What had long been referred to as the “contemplated driver’s license bill” finally passed both houses and was signed Nov. 15, 1935, by Gov. James V. Allred. The new law required “any person driving a car” to have a license as of April 1, 1936; those caught driving without one were subject to a $200 fine — equivalent to more than $3,000 in today’s money.
Drivers had to be at least 18 years old and pass a test. There was no fee for regular licenses, which were “notarized free,” and chauffeur’s licenses cost $4.
The information above was taken from a San Antonio Express – News article.
A Lady Observing The Machine Make Drivers License’s In The 1970’s. 
Angora Chronicles 