As with most of Sinners, there are several things going on at different levels. The choice of "Will Ye Go, Lassie, Go?" has meaning within that particular scene, and the choice of British folk music has meaning within the broader narrative.
The use of "Will Ye Go, Lassie Go" is somewhat anachronistic, in that it was first recorded in 1957, 25 years after Sinners takes place. This is entirely forgivable: The song is based on a much older one called "The Braes of Balquither", which has a similar tune and lyrical content. It's possible, as noted in the Wikipedia article, that the modern version was written much earlier and simply not recorded until the 1950s. I surmise that the producers hand-waved the anachronism away because today's audiences are more familiar with the modern version of the song. (Within the narrative, we might speculate that the 1957 recording was influenced by the characters who survive until the epilogue.)
"Will Ye Go, Lassie Go" is about enticing a lover to come out into a wild place and be together in nature by constructing a memorial to her:
I will build my love a bower
By yon clear crystal fountain,
And on it I will pile
All the flowers of the mountain.
Will you go, lassie, go?
One key difference from the original "Braes of Balquither" is that the chorus invites others to join a community of practice, each collecting wild flowers for their own respective dearies:
And we'll all go together,
To pull wild mountain thyme,
All around the purple heather.
This "group activity" aspect is reinforced by the particular arrangement used in Sinners, where all three members of Remmick's troupe take verses singing, and join together in the chorus.
In the last verse, the singer hints that the listener may become the object of his affection in time:
If my true love she'll not come,
Then I'll surely find another,
To pull wild mountain thyme,
All around the purple heather.
Will you go, lassie, go?
So, Remmick and his troupe are enticing Mary with the antithesis of what Stack represents to her:
- A life roaming outdoors instead of tied to a single building
- A lover who stays true to her for a long time
- A cultural tradition rooted in the British isles, rather than West Africa
Given Mary's personal history with Stack, and her status as a "passing" white with mixed heritage, we can see why the song affects her as much as it does. The synthesis between these alternatives -- a life with Stack while he runs a juke joint, and a life roaming about with Remmick -- comes in the epilogue.
On a broader level, the use of British folk and American "roots" music for Remmick and his band calls to mind the history of rock 'n' roll, country music, bluegrass, and other American popular forms, all of which trace a mixed heritage to both the British Isles and Africa. "White artists and record producers got rich stealing from black artists" is an oversimplification of that history, but one that can be read in Sinners: When Remmick first turns up at the juke joint, he claims to stand for "music and equality," which sounds like something a 1990s A&R man might say while signing a hip-hop act. By the end of the night he reveals his true hunger to Preacher Boy: "I want your memories! I want your SONGS!"
