Preheat the oven to 375 degrees F.
Make a bread bowl by cutting off the top third of the loaf of bread to expose the inner crumb. Use your fingers to tear out the crumb, trying to keep it in large pieces. Cut or tear the crumb of the bread into 1 1/2-inch pieces. Place the bread bowl and the bread pieces on a baking sheet and bake until slightly dried out and lightly toasted, about 10 minutes.
Put the leeks in a large bowl of water and wash thoroughly; drain.
Melt the butter in a large saucepan over medium heat. Add the leeks, garlic, cayenne, salt and pepper to taste and cook, stirring occasionally, until very tender and golden in parts, about 10 minutes. Add the milk and bring to a simmer. Add the cream cheese and goat cheese a few spoonfuls at a time, stirring well after each addition, until all of the cheese is smoothly incorporated. Continue to cook, stirring, until the dip is hot, about 3 minutes more. Stir in the dill, lemon zest and juice and season with salt and pepper. Transfer to the bread bowl and garnish with the dill sprig. Serve with the toasted bread and vegetables for dipping. Top with bread top as decoration.