Combine first 3 ingredients in a heavy saucepan over low heat. Gradually add lime juice, stirring constantly; add butter, 2 tablespoons at a time, stirring constantly after each addition until butter melts.
Cook stirring constantly, 10-15 minutes. Serve immediately over fish. Makes 1 cup.
To reduce fat and calories, substitute 1/2 cup egg substitute for 4 eggs and reduced-calorie margarine for butter. Cook according to directions. Pour into container of an electric blender, and process on High for 2 minutes.