One possibility is that Aslan is....Aslan. The Chronicles of Narnia is a Christian allegory with Aslan fulfilling the rulerole of the triune God of Christianity (in The Lion, Witch, and The Wardrobe he is primarily representing God, The Son).
Does Aslan want Edmund to die? No, therefore Aslan's will is carried out and Edmund is not killed by the White Witch. In Christian theology, God's will, purpose, and plan is always fulfilled. Even when it looks like evil is getting their way (the story of Job or Joseph), God is restricting their actions and/or using them for His purposes.