I learned "Lady on the Green" from Cathy Barton-Para's class on Midwest square dance tunes at Elderly Instruments' Midwest Banjo Camp 2017. The banjo tab is Cathy's. The standard notation is from www.abcnotation.com with a number of corrections.
When you play the first phrase of the A part slowly (as we did in the class) it turns out to be very similar to the old Scottish children's song "Three Craw Sat Upon A Wa'".