Why doesn't Edmund backup Lucy's story about Narnia?

Answer 1

It's because Lucy was already in Narnia when Edmund came in. She was busy visiting Mr. Tumnus (the fawn) while Edmund was talking to the White Witch. They only saw each other after Lucy's visit and Edmund's conversation with the White Witch.

Answer 2

Edmund initially doesn't back up Lucy's story about Narnia because he is ashamed of the lie he told to the White Witch and fears that admitting the truth would expose his deceit. It's not until later when he realizes the importance of supporting his siblings and the truth about Narnia that he confesses to his own experience in the magical land.

Answer 3

Perhaps for two reasons: 1. He did not want to admit he had been wrong and Lucy had been right. 2. He wanted to keep Jadis's throne to himself.