I've found songs containing the words

"grasshopper sittin' on a sweet-potato vine"
"grasshopper sittin' on a railroad track" and
"jaybird sittin' on a hickory limb"

but nothing with the words

"grasshopper sittin' on a hickory limb".

Furthermore, neither "grasshopper sittin' on" nor "sittin' on a hickory" turned up in any book by anyone named Lomax, although several books by John and Alan Lomax are indexed by Google.