At first glance it opens*, but that depends on if the ‘string’ attached to the lid gets wound** around the spindle of the last cog/sprocket or not. If it does then it opens, if in fact it winds round a bit and then slips off the end and goes slack as it comes back round then the lid will oscillate.
if ** is true then * is true eventually no matter what direction it turns, but if it goes the ‘other’ way to the image then it would initally close a bit, then open and keep opening as the string wound round the spindle the other way.