Bob Coltman and wife have done a good job of identifying the correct "Glory of the Lamb" gospel song; that title is much used and there are about a dozen in current use.

The version by the Kentucky Ramblers (1930s) is the earliest dated recording I can find (their work deserves to be better known). Their "Glory to the Lamb" is on cd, Paramount Old Time Recordings, disc 3, track 24.

As both Lighter and I have posted, the Salvation Army would never have sung the parody and it should never be listed as a SA song.

I have some old gospel books and will check them later, but I don't think the song is old.