To determine whether or not “The Lottery” is interpretive fiction you must ask yourself, does this story’s theme challenge our beliefs and provide somber truths? A reader need not accept a theme that is contrary to his or her personal beliefs. However, any theme is worthy of consideration in that it is someone's view. Does this story have a meaningful realistic plot, conflict, setting and characters? Some critics believe it is a parable and "the shocking ending prompts readers to think about the moral implications of the lottery and how such issues relate to society as a whole." I this is the way you view the story then the answer to your question would be yes.
I have always thought of “The Lottery” as more of a speculative fiction, as in "what if this really happened." What would I do? How would I handle dealing with this tradition? The theme of this story is a community which refuses to let go of tradition, no matter how terrible that tradition is and the “Lottery” is performed as commonplace as any other activity in the town. It is accepted as readily as the yearly prom, an election, or any other annual occurrence.
As the previous answer pointed out, the answer to this question could go either way. It is possible to read "The Lottery" as a piece of pure escapist fiction. Readers are taken to a fictional setting and are more or less "entertained" at the unfolding events. The entertainment for readers might not always be fun, especially the ending, but not all readers are going to interpret anything deeper out of the story other than it being a story with a sad ending.
I do believe "The Lottery" is an example of interpretive literature. The main idea that we pick apart and interpret deals with tradition. The town in this story practices a horrible tradition of stoning a town member to death. Most first time readers of this story do not even catch why the person has to die, but Old Man Warner does drop a hint about halfway through the story:
"Used to be a saying about 'Lottery in June, corn be heavy soon."
However, it is clear that Old Man Warner is the only person alive who has any recollection of why the lottery was initially started. Now the lottery is a tradition that the town keeps for the sake of keeping a tradition. This concept can bring in a lot of interpretation and discussion. Should traditions be kept because they are traditions? Can they change? Is it okay to stop a tradition? When? When does morality outweigh tradition? Are there any current traditions, in real life, that perhaps should be changed/stopped? All of those questions are raised by this Jackson story, and for that reason I believe the story is a good example of interpretive fiction.