I'm confused about what you guys are talking about now :(

There was a chantey, with the chorus "Lowlands Away, my John". Some texts talk about dreaming a visit from a lover. Some are more gritty, about working conditions and low pay. All versions I've seen have a similar melody, albeit since it is a flowery and rubato sort of thing, the transcriptions look superficially different.

[Side note: The same melody has appeared in different modes, major and minor. I am very curious about this, something I wonder may have stemmed from a transcription error.]

Grainger set a concert choir arrangement of the chantey, culled from two collected interpretations. IMHO this a a weird place to start an inquiry into the trajectory of this chantey, but it happened to be what the OP was interested in :)

Claire brought up Baez's version, which is interesting so far as it has us think about what sort of sources she was using. Textually, she is without doubt singing the chantey. Melody-wise, she probably took a lot of artistic license with the customary tune, however, and she has sung it in a way that is decidedly not chantey-like. Big whoop, people do that all the time. Plus, the song has/had life as a non-chantey, anyways (although not sung to the "dollar" lyrics).

Q brought up another "Lowlands" song that has no bearing on this discussion. I see a common methodology in your discussions, Q, which is to stick to particular words and search the hell out of them. Sometimes it works, sometimes it dont.
Other chanteys with "Lowlands" phrase are "Lowlands Low" (a rare piece collected by Hugill and Sharp), the "Golden Vanity" (an older English ballad that has given birth to many forms), and "The Five Gallon Jar" or "Larry Marr," which seems to borrow the "lowlands" phrase ~I think~ from a minstrel tune (I don't remember off the top of my head).

The "other" song by Baez that Q originally mention, WHOEVER sang it, based on the lyrics, looks like a version of "Golden Vanity" -- a ballad about pirates, related to "Turkish Revelry" etc. In any case....completely unrelated....

Where am I off?