My guess is it's a home-made linisher or belt sander.
On the left, a large drive pulley is missing. A complete device would drive an abrasive belt over the two rollers at left front. The chisel thing marked 'Support' supports the underside of belt when work is being sanded: possibly the chisel held a platform which is also missing.
The precise height of the belt relative to the chisel/platform is controlled by the dial handle. This part of the device is an adapted slide.
On the right, the bolt and nuts are either a temporary drive handle or a dog intended to be driven by the lathe's faceplate.
The photo is a rear view, and in operation the belt would be on the right, and the arm adjusted more vertically, something like this commercial example.
My feeling is it's a lash-up of parts rather than a commercial product or kit. Someone making the best of what he could get hold of. Dates back to the time when lathes were accessorized enthusiastically because workshops were tiny and power tools expensive.
Today small belt sanders are under £100. My guess is a new one would out-perform BASS666's fully refurbished device and be a lot more convenient! Assuming my guess is correct that is! Although I'm not impressed by the device itself, the parts it's made of are useful. The swivelling do-dah is well worth having on it's own.
Dave