A text search of Thomas W. Talley's "Negro Folk Rhymes" does yield one, and only one lark reference, but it's an interesting one, either a song or a spoken rhyme. He fancifully calls it "Antebellum Courtship Inquiry," but it might, to the singer(s), have been known as something like "Flyin' Lark, Settin' Dove":

    (He) Is you a flyin' lark or a settin' dove?
    (She) I'se a flyin' lark, my honey Love.
    (He) Is you a bird o' one fedder, or a bird o' two?
    (She) I'se a bird o' one fedder, w'en it comes to you.
    (He) Den, Mam:
            I has desire, an' quick temptation,
            To jine my fence to y[o]' plantation.

Here the lark is the woman, apparently more exciting and adventurous than the domestic dove, but since she's a bird of one feather, she'll be faithful all the same, so he elects to choose her.

In the "Poontang Little" context it's not clear who the lark is, the man or the woman, but I think it may be the man. (Geese are female, of course, vs. ganders, but the word is also used for both sexes.) It might even be an implied "other man," I'm not sure.

Bob