When and how do readers know that Mrs. Sappleton's niece has been lying? Once it is revealed that she has been lying, can anything be found...

The readers do not know that Vera was lying until Framton Nuttel has fled from the house and is running down the road in flight from the three figures he took to be ghosts. Then Mr. Sappleton reveals that they are not ghosts but only three hunters returning for tea from a day's shooting.

"Here we are, my dear," said the bearer of the white mackintosh, coming in through the window, "fairly muddy, but most of it's dry. Who was that who bolted out as we came up?"

A few faint clues that Vera was lying can be found after the readers realize that her story was a practical joke. For one thing, Vera asks Framton Nuttel two questions to find out how much he knows about her family and about the locale. These questions are:

"Do you know many of the people round here?"

"Then you know practically nothing about my aunt?"

Readers might assume that the girl is just making polite conversation, but in retrospect they will realize that Vera needed to be sure Framton Nuttel knew nothing about her aunt or about local history before she could proceed to tell him her ghost story.

Readers will also see that Vera was intentionally planting a suggestion in the visitor's mind when she says:

Do you know, sometimes on still, quiet evenings like this, I almost get a creepy feeling that they will all walk in through that   window--" 

Note that the girl is not trying to plant a suggestion in the readers' minds, because she isn't aware of the existence of any readers; but the author is very deliberately planting that suggestion in the minds of his readers. When the three figures appear outside walking towards the open window, they will be doing exactly what Vera foreshadowed. Obviously it is Saki's intention to frighten the readers of his story. They will be identified with Framton Nuttel because the story is told through his point of view, and they will suddenly be afraid they are going to be witnessing a horrible scene in which a trio of decaying walking dead men will enter the living room all carrying shotguns. 

This little scare only lasts a few moments before the readers realize that these are just ordinary mortals and that Vera had cast them all, along with her aunt and herself, in an elaborate play intended to frighten poor Framton Nuttel out of his wits. Vera may not have expected Framton to react so strongly. She did not know he was suffering from a nervous disorder until she heard him talking about it to her aunt. He hadn't said anything about his "nerve cure" to the girl because it would not have been appropriate. But once the cat was out of the bag, so to speak, there was nothing Vera could do but wait and see what would happen when the three men returned for tea.

Framton would have had no time to say anything to Vera about his nerves or his nerve cure anyway. As soon as the girl finishes her story and tells him in a spooky manner that she sometimes gets the creepy feeling that the men will return from the dead, her aunt arrives and takes over the hostessing.

She broke off with a little shudder. It was a relief to Framton when the aunt bustled into the room with a whirl of apologies for being late in making her appearance.