The Crapshooter's Blues has a funeral request that is very close to "The Unfortunate Lad" and Blind Willie McTell's version also has the "head is aching, heart is breaking" line found in many versions of "Bad Girls Lament".

I think it's relationship to "Unfortunate Lad" is more obvious than that of "St. James' Infirmary".

Here are the interesting parts from Crapshooter's Blues:

Sixteen real good crapshooters
Sixteen bootleggers to sing a song
Sixteen racket men gamblin'
Couple tend bar while i'm rollin' along

He wanted 22 womens outta the Hampton Hotel
26 off-a South Bell
29 women outta North Atlanta
Know little Jesse didn't pass out so swell

His head was achin', heart was thumpin'
Little Jesse went to hell bouncin' and jumpin'
Folks, don't be standin' around ole Jesse cryin'
He wants everybody to do the charleston whilst he dyin'