Lemon extract comes from lemon peel, not lemon pulp. It consists mainly of lemon oil, alcohol and water. It’s nowhere near as acidic as lemon juice, so it won’t cause milk to curdle.
Whether to use milk or citrus juice in the glaze depends on what effect you’re aiming for. If I were glazing a lemon cake I would use citrus juice. If I were glazing a carrot cake (for example) I would use milk.