If anyone (20+ years later!) is still trying to find out where Lucy Simpson got the tune she sang, here's what she wrote in the booklet of the album:

"Blessed Quietness" was collected for me by my subconscious in the summer of 1975. I was attending my first Folk Music Week at Pinewoods Camp in Plymouth Massachusetts, and had reached the fifth day of frantic feasting on classes, workshops, concerts, all-night singing, and non-stop tunes drifting through the woods as musicians practiced, swapped, and jammed. I had hardly slept a wink and was definitely on the verge of collapse.

I tried to nap in my cabin, but was over-stimulated and unable to relax. Reaching for something to read (I had brought only songbooks), I started to learn "Blessed Quietness." I didn't notice until the next day how exactly appropriate it was to the situation. It has been my favorite hymn since then. The hymnal was The Golden Trumpet, published by the Christi Witness Co. of Chicago. No date of publication is given, but the song copyrights range from 1882 to 1906.
Mrs. Manie Payne Ferguson is cited as writer of the words, and William J. Kirkpatrick is credited for the music. I've seen it in other hymn books with another (far less satisfying) tune. (L.S.)

The full LP liner notes and booklet are at https://folkways-media.si.edu/docs/folkways/artwork/FLG00086-LP.pdf .