Preheat oven to 350°. Sift flour, baking powder, and salt into a medium bowl; set aside. In the bowl of a stand mixer, beat sugar and 1/2 cup butter until creamy. Crack eggs into a small dish (do not beat) and add vanilla. Add eggs to the butter mixture 1 at a time, scraping down the inside of the bowl as needed. Beat in flour mixture and milk in alternating batches, starting and ending with the flour and making sure each addition is fully incorporated before adding the next. Stir zest into batter.
Butter and flour a 5- by 9-in. loaf pan and pour in batter.
Bake 45 minutes, or until a toothpick inserted in the center comes out clean. Cool 5 minutes, then invert cake onto a rack. Remove pan and let cake cool to room temperature, at least 40 minutes.
Meanwhile, make lemon curd: In a heavy-bottomed medium saucepan, melt butter with lemon juice over high heat. In a medium bowl, whisk together sugar and yolks. Slowly whisk hot lemon butter into egg mixture, 1/2 cup at a time. Pour mixture back into saucepan and cook, whisking constantly, until the mixture is very thick, 5 to 8 minutes.
Transfer lemon curd to a glass or plastic container. Cover with plastic wrap, pressing it onto the top of the curd to prevent a skin from forming. Chill until cold, at least 1 hour and up to 2 days.
Make meringue: Whisk whites and sugar together in a medium metal bowl. Set over a saucepan of simmering water and whisk constantly until mixture is warm to the touch and sugar feels dissolved, about 2 minutes.
Scrape whites into the bowl of a stand mixer. Whisk on high speed until light and fluffy and the side of the bowl feels cool to the touch, about 2 minutes.
Assemble cake: Preheat broiler, positioning oven rack about 7 in. from the heat source. Using a serrated knife, trim brown exterior from sides and top of cake. Slice cake horizontally into 3 even layers.
Place 1 cake layer on a rimmed baking sheet. Spread with half the lemon curd mixture. Repeat with second layer and remaining curd. Top with last layer. Using a spatula, cover the entire cake with the meringue.
Broil cake just until top is golden brown, being careful not to burn it, about 1 minute. Using 2 large pancake turners (sliding 1 under each side of cake), transfer cake to a serving plate.