In the story The Open Window, Vera (a fifteen year old girl) is waiting in her home for some relatives when she receives he visit of Mr. Frampton Nuttel, who was visiting the country side as a way to cure his nerves, and was going to spend time with them.
Vera tells him a story about tragedy and romance, drama, and suspense about her relatives that totally enthralls Mr. Nuttel. Yet, to answer your question, Vera did not have to deceive Mr. Nuttel: She simply did it because, as Saki says at the end of the story, Vera's specialty was to tell stories which were "romances at short notice."
In other words, Vera simply could not resist. She saw that the man was, in essence weaker than herself. She saw in him a potential good listener to a made up story, and since she loved telling such stories, she also saw in him a victim of her little pranks.
Hence, to answer your question Vera didn't much HAD as much as she WANTED to deceive Mr. Nuttel as a young, picaresque and creative, dramatic teenager that she is.
There is unclear reason why Vera has to tell him a lie. But, possibly, she does it because it's her talent as the writer indicates at the end of the story and her characteristics. Additionally,she finds that Mr. Nuttel is a outlander and easy to hoax. it seems that she often does it as she lies again when her relatives ask why Mr. Nuttel has to run away when they come up. It might be she is just fifteen years old, the age that'd rather live in the imaginative world