- FOR THE CAKE: Preheat oven to 350ºF. Butter two 9-inch-square nonstick cake pans with 2-inch-high sides; line bottoms with parchment paper; butter paper.
- Sift flour, baking powder and salt into medium bowl; set aside.
- Using an electric stand mixer and paddle attachment, beat butter in large bowl until fluffy. Gradually add sugar, scraping down sides of bowl occasionally and beating until light. Beat in lemonade concentrate, zest and vanilla. Beat in eggs one at a time, scraping down sides occasionally. Continue to beat until mixture is smooth.
- On low speed beat in dry ingredients alternately with milk in 3 batches, beginning and ending with dry ingredients, until just blended. Divide batter equally between prepared pans.
- Bake cakes until tester inserted into center comes out clean, about 25 minutes. Cool cakes in pans on racks.
- FOR THE FROSTING: Using electric stand mixer and whisk attachment, beat cream cheese and butter in large bowl until light and fluffy. Gradually beat in sugar, scraping down sides of bowl occasionally. Beat in zest, vanilla and lemon oil until mixture is smooth and fluffy, about 4 minutes.
- TO ASSEMBLE: Turn cakes out onto work surface. Peel off parchment paper. Place one cake layer, flat side up, on platter. Spread with 1 cup frosting. Top with second cake layer, flat side down. Spread remaining frosting over top and sides of cake.
- DO-AHEAD TIP: Cake can be made 1 day ahead. Cover with cake dome; refrigerate. Let stand at room temperature 2 hours before serving.
- OPTIONAL GARNISH: Peel off long strips of lemon zest using zester. Sprinkle zest around edges of cake.