As the title of Shirley Jackson's story suggests, Miss Strangeworth is not actually lying, but only asking questions about the possibility of certain things happening. For example, she has written to the parents of Linda Stewart suggesting the possibility that their daughter may be going too far with her boyfriend Dave Harris. We don't know the text of that letter, but the three letters she writes in the course of the story all contain questions intended to plant seeds of suspicion in the recipient's mind. Miss Strangeworth may truly be having these suspicions herself, so she would not be exactly lying.
She writes to Don Crane:
Didn't you ever see an idiot child before? Some people just shouldn't have children, should they?
She knows that both Don and his wife are worried about their six-month-old daughter's development. Notice the question marks. This old lady is not making accusations but raising questions.
She writes to Mrs. Harper:
Have you found out yet what they were all laughing about after you left the bridge club on Thursday? Or is the wife really the last one to know?
Again, questions not statements. Mr. Harris might be having an affair, and everybody in town might know about it. These are possibilities. Miss Strangeworth probably belongs to this bridge club and heard a lot of women laughing about something.
Miss Strangeworth writes to old Mrs. Foster, who is going to have an operation:
You never know about doctors. Remember they're only human and need money like the rest of us. Suppose the knife slipped accidentally. Would Doctor Burns get his fee and a little extra from that nephew of yours?
Again, there is at least a possibility that Mrs. Foster could die on the operating table and that her nephew would be happy if that happened.
Miss Strangeworth is apparently motivated by the belief that it is her responsibility to look after all the people in her town. Her letters are sincere warnings. In the case of the Cranes, she may be warning them not to have any more babies.
Many people seemed disturbed recently, Miss Strangeworth thought.
This sweet little old lady is really a horrifying woman. She really has no idea how much unhappiness she is causing.