The advantage of this lamp over a spring powered wound clock would be that it emits light. The disadvantage is that it's comparatively poor at keeping the time.
True, but my question is if a clock winding mechanism can keep going for days without need of winding could a clock winding style mechanism be more efficient than a gravity weight powered one.
SCNR. I suppose the advantage of clock winding mechanisms is that they can deliver (mechanically) a constant, relatively low level of power. Compared to an LED, a wristwatch uses very little power (about 1µW according to Wikipedia). Of course this lamp may be more comparable to a grandfather clock than a wristwatch; I don't know how much power a grandfather watch requires, but the energy you store winding it up can't be that high since it's not that much work, and the strength of the mechanism is that the stored energy is then delivered over a long time, ie. days.
Also, with clocks, you get to skip the conversion of the energy completely. That immediately gets you a much higher efficiency than this lamp, which is potential energy converted to electricity (losing heat), converted to light (losing heat). Of course energy transmission losses still apply, ie. it's not free to get the mechanical energy from the spring to the hands of the watch.