I need to write a teaser with NO spoilers in order to capture peoples attention for them to want to read these 2 short stories. It has to be 2 separate teasers.

The question mentions two stories; however, I only see reference to Shirley Jackson's "The Lottery." I can help with a teaser about that particular story.
I am not sure how long your teaser needs to be. It does make a difference, because some educators think "teaser" and "tagline" are essentially the same thing. I do not consider those two terms interchangeable. A "tagline" is one sentence that is intended to peak audience attention. A tagline is often very vague. "Just when you thought it was safe to go back in the water" is the tagline from Jaws 2. It's an interesting line, but it doesn't really tell anything specific.
For your teaser, I think that you are being asked to write a brief paragraph about "The Lottery." It would be similar to something that you would read on the back cover of a book or the back of a DVD movie box. "The Lottery" starts in a fairly happy and cheery way. A town of people is gathering in a town square for some kind of traditional festivity. The story ends in a horribly graphic way. One of the townspeople is stoned to death because of an archaic tradition. That's where you want to lead your reader with your teaser. I can't write your teaser for you, but perhaps you could start it off like the following:
"In a village that harbors strange traditions, people gather at the town square. A box is placed in front of the gathering crowd, and names are called one by one. As each name is read, a mixture of relief and apprehension slowly makes its way through the crowd."