Combine strawberries and 2 tablespoons sugar in a bowl; cover and refrigerate until ready to serve.
Preheat oven to 400 degrees F (200 degrees C).
Combine flour, 2 tablespoons sugar, baking powder, and salt in a bowl. Cut in butter with a knife or pastry blender until mixture resembles coarse crumbs. Whisk milk, egg yolk, and 3/4 teaspoon lemon zest in another bowl; stir into crumb mixture until dough is moistened. Turn dough out onto a lightly floured surface and knead 10 turns. Divide dough in half; pat or roll out into a 3/4-inch thick round. Transfer rounds to a baking sheet.
Bake in preheated oven until golden brown, 8 to 10 minutes. Remove to cool on a wire rack for 15 minutes. Split each shortcake in half horizontally.
Mix yogurt, sour cream, agave nectar, and 1/2 teaspoon lemon zest in a bowl; set aside. Beat whipping cream in another bowl until foamy. Add 1 teaspoon sugar, continuing to beat cream until stiff peaks form. Lift your beater or whisk straight up: the egg whites will form sharp peaks.
Arrange cake bottoms on dessert plates and evenly spread with yogurt mixture. Top each cake with 1/4 of the strawberries and 1/4 of the whipped cream. Place the cake tops over the whipped cream and cover with remaining strawberries and whipped cream.