The Homer Lee Bank Note Company was located in New York City. They were absorbed into the American Bank Note Company by 1891, so your box could predate that. Maybe it was sold as a souvenir item near the area depicted on the cover. It appears to be paper or celluloid(?) covered, perhaps intended for storing mounted photographs? It might have been a companion piece for a matching photo album?
Lots of maybes and mights here...In other words; I'm guessing.