It definitely sounds like lola or loller, and I could buy the explanation about lull. Truthfully I think Darby and Tarleton only heard the song second- or third-hand and were just mumbling along.

In my opinion, it always helps to go to the source, so here's my transcription of George Reneau's Birmingham (listen)

BIRMINGHAM
(as recorded by George Reneau)

I have traveled east and west
Stopped at Washington for reset
I had an interview with Uncle Sam
And he said to me that day
"Do not throw your pep away
For the next World Fair will be in Birmingham"

CHORUS
Oh, Birmingham, you're sure to win the prize
The swiftest little town in Alabam'
San Francisco was a lala* til she lost her bottom dollar
She'll never make a town like Birmingham

I have traveled over Asia
New York and Australia
I went to see a corner of Japan
And the King of Queen of Spain
Invited me again
Just to hear some more about old Birmingham

CHORUS

If you don't believe it's true
I'll just tell you what to do
Just ask the man you know who's always right
He will tell you in a minute
San Francisco isn't in it
But old Birmingham is simply out of sight

CHORUS

* lala - late 19th/early 20th century slang for "a swell," which was a word of multiple definitions at the time, but primarily, either a gentleman, a specimen of exceptional renown, or something that was first-rate (A dictionary of slang and colloquial English, Farmer and Henely, pp. 259, 459). It's my belief the singer slurred this word a bit to rhyme internally with dollar.