Prepare Classic Genoise as directed in a 9-inch springform pan, adding 1 teaspoon lemon rind to batter. Cool cake completely.
To prepare buttercream frosting, beat butter and next 3 ingredients (butter through cream cheese) at medium speed of a mixer until smooth. Lightly spoon powdered sugar into dry measuring cups; level with a knife. Gradually add powdered sugar to butter mixture; beat at low speed just until blended (do not overbeat). Cover and chill.
To prepare lemon syrup, combine water and granulated sugar in a small bowl; stir until sugar dissolves. Stir in lemon juice; cool to room temperature.
To assemble the cake, split the Classic Génoise in half horizontally using a serrated knife. Place bottom layer, cut side up, on a serving platter, and brush with half of lemon syrup. Spread with 3/4 cup frosting. Arrange 3/4 cup raspberries on top of frosting. Top with remaining cake layer, cut side down, and brush with remaining syrup. Spread remaining frosting over top and sides of the cake. Top with 3/4 cup raspberries. Store cake loosely covered in the refrigerator.