Preheat oven to 350°F. Coat a 9-by-13-inch baking pan with baking spray.
Whisk 4 eggs, 1 cup sugar, ¾ cup buttermilk, ⅔ cup oil, 2 tablespoons lemon zest, 3 tablespoons lemon juice, 1½ teaspoons vanilla and ¼ teaspoon salt in a large bowl until smooth and well combined.
Add 1 cup all-purpose flour, 1 cup whole-wheat flour, 1 teaspoon baking powder and ½ teaspoon baking soda; fold until just combined.
Transfer the batter to the prepared pan. Bake until a wooden pick inserted in the center comes out clean, 25 to 30 minutes.
Let cool completely in the pan on a wire rack, 1 to 2 hours.
Meanwhile, prepare frosting: Beat the softened butter and cream cheese in a large bowl with an electric mixer on medium-high speed until creamy, about 1 minute.
Add 1½ cups confectioners’ sugar, 2 teaspoons lemon zest, 1 tablespoon lemon juice and ⅛ teaspoon salt; beat on low speed until combined.
Increase speed to medium-high and beat until light and fluffy, about 1 minute.
Spread the frosting evenly over the cooled cake. Garnish with lemon slices and/or additional lemon zest, if desired.
