There is far more to democracy than the simple following of the wishes of the majority - one of the main tenets of democracy is the rule of law and equal rights before the law.  As such a group of people calling for the execution of an individual without the due process of law would not be a democratic decision.

Whether or not a democratic decision would be open to calls for that decision to be overturned brings into play yet another of the ingredients of a democracy - the right to free speech, the right to criticise decisions made and those who made them.