Janie, you are confusing "Oh, Eliza, Little Liza Jane" (Ada de Lachau-Earl Fuller or possibly tradition as PoppaGator suggests), with "Good Bye, Liza Lane" (Eddie Fox 1871 or possibly earlier traditional fiddle tune as some have suggested- "Minstrel Songs, Old and New," Oliver Ditson & Co., lists Eddie Fox as arranger).

For the latter, see (DT Study)Lyr. Req.: Goodbye Liza Jane, linked at top of this thread. AKA 'Goin' Down to Cairo," etc.

Later musicians have sometimes joined the two. Did one give rise to the other? Use of one as a fiddle-dance tune and the other as one of the signature New Orleans marching songs seems a good division to me.