Sound clip of "Lay the Lily Low" (guitar version) by Charlie Byrd on Mr. Guitar (the album Sorcha linked to above) is HERE (CD Universe).
From Timothy P. Lynch, Strike Songs of the Depression (University Press of Mississippi, 2001, pp. 141-142):
Regarding the hymn used as the model for "Which Side Are You On?," there is some confusion. In her interview in Stanford, "'Which Side Are You On?," 15, Reece related, "I've heard different people's ideas on where I got the tune for 'Which Side Are You On?,' but I think I got it from a hymn called 'I'm Going To Land On That Shore.' The first verse starts out, 'I'm gong to land on that shore / And be saved forever more,' but I don't remember more, and I've looked everywhere." In Kahn, Hillbilly Women, 37, Reece said, "The music to the song is an old hymn. I can't remember what was the hymn, but I've got to look in the songbooks and find out what that was a tune to." In the liner notes to They'll Never Keep Us Down: Women's Coal Mining Songs (Rounder Records 4012, 1984), 4, she gave the tune as "Lay the Lily Low." In Greenway, American Folksongs of Protest, 169-70, the tune is also given as "Lay the Lily Low." However, folklorist Archie Green maintains the tune is most likely related to the broadside ballad "Jackie Frazier." Regardless as to the particular song used as the model, it was a song in the mountian tradition familiar to the people.
"Jackie Frazier (Jackie Monroe, Jack the Sailor)" is in the DT, and in the Max Hunter Collection (Click here). It is the model for Bob Dylan's "Jack-a-Roe". There're few similarities in melody.