A most unusual little lathe: cast in bronze - and of a decidedly crude appearance -  it displays design feature common to lathe of the mid 1800s and earlier. Arranged with its spindle supported by a single plain front bearing (presumably using the material of the headstock) the rear was held against an adjustable hardened point The 2-step pulley was intended to take the usual round leather belt - probably driven by a "foot motor" or even a hand-turned bench flywheel.
Formed as an open box, the tailstock looks absolutely contemporary of the era the design also being found on much larger lathes.
Could this be a commercial effort or something cast as "homework" in a foundry by an enthusiastic but impecunious model engineer or clockmaker? Unless an advertisement from the period showing the lathe is discovered, we shall probably never know.