The square shank suggests its for a bit and brace not a lathe?
Clearly a cutter that can be adjusted inward
Sliding part appears to be a square dovetail
Patent date Dec 5 1911 perhaps.
This photo is a bit fuzzy, sorry.
I have no idea what this tool is - listed at https://www.trademe.co.nz/3703975458
Best guess is a groove cutter for a hand drill?