We do have two songs here, as richr pointed out. SINSULL has added a third (interesting, though; the "Look out, lady ..." lines are new to me).

There may be a conection way back when, if 'gentleman' or 'palmer' is changed to Jesus.
There is a Coptic song (on youtube) about the Samaritan woman (El-Samaria)at the well; use of the myth (John 4) in song seems to be old. No translation of the Amharic(?) of the Coptic song. There is a full choral mass setting by Gouzes.

Did Dave van Ronk compose the modern 'Jesus met...' song? The lyrics in "Rise Up Singing" (Sing Out book) seem to have a Af-Am gospel slant, but I haven't found the song in any of the gospel sites.