Imagination is something that is dangerous for Lyra precisely because she lives in a dangerous world where she is part of the plans and machinations of dangerous characters, such as her father, Lord Asriel, and her mother, the sinister Mrs. Coulter. It is the combination of Lyra's imagination and her intellilgence that make her aware of the kind of world she is in, such as the way that she very quickly works out what the Master did in the opening chapter when he adds the powder to the bottle of wine:

Don't you remember, he made the Butler leave the room before he did it? If it was innocent it wouldn't have mattered the Butler seeing. And I know there's something going on--something political. The servants have been talking about it for days. Pan, we could prevent a murder!

Lyra here reveals the way that her imagination is in danger of getting her involved in things that are so much bigger and greater than she could ever imagine or dream of. Lyra, as most intelligent children are, is naturally curious, and this works together with her imagination and intelligence to become very dangerous for her, as it leads her to becoming involved in issues and developments that threaten not only her life, but the lives of those she holds dearest.