Make cake: Preheat oven to 350°F. Butter 2 9-inch round cake pans. Cut 2 circles of parchment paper to fit pans and place in bottoms. Butter paper and sprinkle pans with flour. Turn and shake pans to coat surface evenly. Tap out excess flour.
Using an electric mixer, beat butter until light and fluffy. Gradually add sugar, beating constantly until well incorporated. Add yolks, one at a time, beating well after each addition. Sift flour with baking powder and salt onto a sheet of parchment or waxed paper. Add dry ingredients to butter mixture in 3 additions, alternating with buttermilk. Beat in vanilla and lemon zest.
In a separate clean, dry mixing bowl, beat egg whites with a pinch of salt until medium-firm peaks form, but don't allow whites to become dry. Fold about a third of whites into batter to lighten, then fold in remaining whites.
Divide batter between pans and bake on middle rack of oven until a toothpick inserted into center comes out clean, about 30 minutes. Cool in pans on a wire rack for 10 minutes, then turn out onto racks to cool completely.
Make frosting: Combine sugar, 1/2 cup water and lemon juice in a small saucepan. Bring to a boil over high heat, stirring only until sugar dissolves. Cook syrup until it reaches soft-ball stage, 234°F on a candy thermometer. Cool slightly. In a clean, dry bowl, using an electric mixer, beat egg whites until frothy. With beaters running, slowly pour in warm syrup. Beat in vanilla, and continue beating until cool and thickened.
Assemble cake: Arrange one cake layer on a serving platter. Spread top evenly with about 1/2 cup frosting. Set second cake layer on top. Spread top and sides of cake with remaining frosting. Gently pat shredded coconut onto frosting around sides and sprinkle coconut generously over top.