The Three-Legged Stool
Critic Helen Nebeker argues that the three legs of the stool are like the three aspects of the Christian Trinity (God the Father, God the Son, and the Holy Spirit); the use of the stool to support the black box thus represents the manipulation of religion to support collective violence (source). It is true that this story is so short that everything in it seems like it must be symbolic of something. Another possibility is that this doesn't have to be the Christian Trinity at all; there are trinities all of the place in various religious traditions, like the three Norse Fates, or the Three Graces in Greek myth. The use of this three-legged stool may serve to underline more generally the ritualistic significance of the lottery as a holdover from generic Ye Olden Days.