Little Liza Jane bluegrass has nothing to do with "O Eliza...," the New Orleans marching tune. "It sticks close to the 19th c. fiddle and minstrel "Good Bye ..."
The very cute one by the Bulla Family verges on the New Orleans tune, an example of the melding of the two, but emphasis quite different. Thanks for this one!

The two tunes have certainly influenced each other- and they do meld. That's why I asked "Did one give rise to the other?" On Youtube but not mentioned by you is the old Bob Wills classic. The Texas string bands may have been the first to meld the two tunes

The excellent playing by Bain and Ungar is mostly "Goodbye ..." with a touch of "O Eliza..." in the 'title' line. It is a good example of how the marching tune "O Eliza..." has influenced the old minstrel and fiddle "Good Bye Liza Jane," without taking it over.