Are there any other reasons why Vera lies in the story besides simply enjoying it?
Vera's behavior in Saki's "The Open Window" suggests that she frequently makes up stories since she does so twice within the tale. When she lies to Framton Nuttel, Vera may be trying to prevent the man who is recovering from a nervous breakdown from staying at her aunt's home. Vera, the only female child in the home, may feel that the newcomer's presence may threaten the amount of attention she may receive from the family. Since Vera lives with her aunt and uncle, it is probable that she is an orphan and, as such, may crave the attention of others. This seems to be demonstrated in the tale she tells her aunt, Mrs. Sapleton, about Mr. Nuttel's supposed terrible experience with a dog. It is filled with exaggeration, and Vera seems to captivate the family with her descriptions. Their reaction and the narrator's subsequent comment about how Vera is quite good at creating "romance at short notice" suggests that she is successful in drawing the attention she craves.
Vera lies and makes up the story because she is good at it and it is entertaining for her. She is quite skilled as an actress and as the author tells us quite skilled at "romance at short notice". Vera is a confident character so her story seems even more believable to poor Framton Nuttel. Ironically enough, Vera's name is very close to the word "veracity" which means truth.