Drama is created by conflict and suspense. Both are easily identified in "The Lottery".
The types of conflict involved in this story are man vs. society (every individual is potentially against the society, but in this case, Tessie Hutchinson ended up as the man), and man vs. system/rule/ritual... whatever you might want to define this as, but we see Tess in conflict with the ritual of the lottery.
Suspense is built as Tessie arrives late. I do find it ironic that she seems more nervous than the others and then ends up being the one. She criticizes the lottery before she is stoned.
Other than the elements mentioned by previous editors, you might consider situational irony. The reader is surprised that the "winner" of the lottery is stoned to death. Foreshadowing is another element--the boys are gathering stones when the story begins. The rituals involving the black box, heads of the household stiffly drawing for their families, and the crowd's anticipation of the victim point to a negative ending. So the twist at the end is quite surprising but quite appropriate.
The image of little Davy Hutchinson being given pebbles to throw at his own mother, Hutchinson's screams, and the crowd descending upon her--all contribute to the irony and horror of a most unforgettable ending.
The story contains two seemingly and readily apparent dramatic elements: horror and shock. The two are not mutually exclusive, though, for the surprise depends upon delaying the concluding information until the very end, and the horror is coincidental with the ritualized public murder. There are others but they play a lesser role and the ending is such a shock that initially, readers complained that it was too shocking. Many readers might suggest it is a metaphor for World War II, but that would pigeon hole the story into a greater narrowly focused intention than the way it probably was intended.