I've been digging into the origins of this song and have learned that it was written by Noah Lewis and recorded by Gus Cannon's Jug Stompers with Noah Lewis on vocals and harmonica back in 1929 or thereabouts. But none of the sources I've found has even asked the obvious question: where did the title come from? The lyrics are about being sent to prison in Nashville. In one version (not the Dead's), the last verse refers to the singer's wife. Could she be the mysterious "Viola Lee"?
The same question about Viola Lee puzzled me no end too so great minds think alike. I have no definite answer but this is my guess. Groups like Gus Cannon & JugStompers often times adapted pre existing songs for themselves. It's well known that Joliet Bound Blues performed around the same time (late 1920s early 30s) has substantially similar lyrics. I was able to find another song vaguely similar called Chain Gang Blues by Ma Rainey. The lyrics follow:
The judge found me guilty, the clerk he wrote it down
Just a poor gal in trouble, I know I'm county road bound
Many days of sorrow, many nights of woe
And a ball and chain everywhere I go
Chains on my feet, padlock on my hand
It's all on account of stealing a woman's man
It was early this morning that I had my trial
Ninety days on the county road, and judge didn't even smile
There were obviously different versions floating around at the time Cannon (Noah Lewis singing) recorded his tune. It is suggestive that Rainey's version centers on a woman rather than men. It's possible there was a variant of this titled Viola Lee by some obscure performer that Cannon or Lewis heard. If Noah Lewis was the songwriter he had a rather careless attitude about song lyrics which might possibly extend to titles. (see para below) I strongly doubt Viola Lee was any legal or other official since that would have invited retribution. By the same token, it wouldn't have been someone Cannon or Lewis knew personally since they wouldn't want their name in a song about jail birds. Oddly enough I have a friend who knew a woman named Viola Lee. She comes from Kentucky so the name may not be that unusual in that region.
Your thought that it might refer to the wife or girlfriend of the jailbirds is also possible. What's interesting about that substitute verse you reference (last stanza in version 1 recorded by Cannon and Lewis) about "fix me supper mama, White Lightning went to my head" is that it is a bit of a non sequitur with the rest of the song. After all the men have been sent off to prison so how is he home with Mama going to bed? Another instance of migrating lyrics occurs in another Cannon song with Noah Lewis called Pretty Mama Blues. In that song the Viola Lee version 2 stanza about "I mailed a letter in the air you know by that I have a friend somewhere" occurs almost verbatim in Pretty Mama Blues. In that song it has a completely different context. These may be stray verses from a different version of the proto song to Viola Lee Blues or more likely just a random verse stuck in there by Noah Lewis. The lyrics on the other songs, Pretty Mama Blues and Going to Germany, that Noah Lewis sang with Cannon are quite disjointed, even more than those sung by Cannon. If he was this casual about song lyrics it is quite possible that he would just grab a song title that appealed to him and apply it whether it fit or not.