The Aleut Barabara?

(but that's Alaskan, rather a long way from NY)

EDIT - P.S.
It wouldn't be anything to do with Black Elk's Earth Prayer, would it?

Earth Prayer

"Grandfather, Great Spirit, once more behold me on earth and, lean to, hear my feeble voice.



EDIT - II.

More seriously, I have found a number of references to the Adirondack Lean-to, which was a Native American type of shelter.