Other than the black box in Shirley Jackson's "The Lottery," what way can deconstructionist theory be applied to the story?

"The Lottery" almost could have been written to explicate aspects of deconstruction. Someone like Derrida would probably object to using the word "applied" to his thought, as if it were a set of rules that could be plunked down on a text, but leaving that aside, let's look at several directions this could take.

What immediately jumps to mind is Derrida's essay "Plato's Pharmacy," in which the word "pharmakon" means both poison and cure. "The Lottery" fits the paradigm of ancient sacrifice discussed both by Plato and Derrida: is the lottery the town's poison, cure, or both? 

Deconstruction looks at silences in a text: what is assumed but not spoken because it is so normative in a culture that it doesn't have to be said? What assumptions in the "langue" (or larger sign system) run so deep that they don't have to be articulated in the "parole" of a particular story? One that leaps out of "The Lottery" is patriarchy: we never once are told explicitly that this a patriarchal society, but that clearly underlies everything that happens: men run the lottery, men control the box. Women aren't even named until the eighth paragraph: the early emphasis is on men and male children. You could take all of this and run with it: what is the connection between patriarchy and violence and domination unspoken in this text?

In the same vein, "The Lottery" almost perfectly fits Rene Girard's "mimesis of envy" theory that says society needs a scapegoat, originally in the form of a human sacrifice, to purify itself of a build-up of aggressions and not tear itself apart. You might discuss what is "silent" in this text as this very envy—people all desiring the same thing—and the aggression underlying this seemingly very placid culture. 

Deconstruction, and here I think of de Man, reads "against the grain." Reading "with" the grain, we are supposed to understand the lottery as governed by random chance, but is it really random that a woman ends up as the sacrifice? How random is this male-controlled lottery? Beyond that, Tessie is the transgressive female voice in this story: she arrives late, having "clean" [think about that word in terms of the pharmakon as poison/purifying] forgotten. She is the one who repeatedly says what nobody else will: the lottery is unfair. What if we see the choice of a woman—and this particular woman—as a symbol of who must sacrifice in patriarchal society, not as a random gender choice?