Preheat the oven to 350°F (180°C) and butter two 9-inch baking pans. Dust the bottom and sides with flour. Set aside.
In the bowl of a stand mixer fitted with the whisk attachment combine the egg whites with the cream of tartar. Whisk at low speed until foamy, about 1 minute. Increase the speed to medium-high and add 1/4 cup sugar gradually. Mix until peaks are just stiff. Transfer egg whites to another bowl. Set aside.
In the bowl of the stand mixer fitted with the paddle attachment cream together butter and sugar until pale and fluffy, about 5 minutes.
In a small bowl sift together cake flour, baking powder, and salt.
Add vanilla extract, poppy seeds, about 1 tbsp lemon zest, and 2-3 tbsp lemon juice to the butter mixture. Whisk until combined.
With the mixer running on low speed add flour mixture in three batches, alternating with the milk. Beat until combined after each addition. After everything is added scrape sides of the bowl and mix for ten more seconds.
Gently fold in the egg whites with a rubber spatula. Don't overmix!
Divide the batter between the baking pans. Bake until the tops are golden for about 40 minutes or until a skewer inserted in the center comes out clean. Transfer to a wire rack. Cool cakes to room temperature then slice layers equally in half with a serrated knife.