Prepare 2 (8-inch) round pans by buttering the sides and bottom. Lightly coat the sides and bottoms of the pans with the ½ tablespoon flour. Discard excess flour. Set the pans aside.
Preheat oven to 375°.
Place egg whites in a medium-sized mixing bowl. Beat until the whites are shiny and form stiff peaks. Set aside.
Place ¾ cup of butter in a mixing bowl and beat on high for 1 minute. Add the granulated sugar and beat again for 2–3 minutes. Pour in the milk, lemon juice, lemon zest and 1½ teaspoons of vanilla. Start the mixer on low and beat the mixture for another minute. The consistency of the batter will be very lumpy and chunky.
In another bowl, measure the cake flour, baking powder and salt. Mix with a fork until the mixture is uniform. Add the dry ingredients to the butter mixture. Beat this slowly for a couple of seconds and then on high for 10 seconds until the batter is smooth and uniform in color.
Add ¼ of the egg whites and mix with a whisk or a fork to lighten the mixture. Add the remaining whites and gently fold them into the rest of the batter. The batter will appear lighter and fluffier and will be fairly smooth.
Divide the batter between the prepared cake pans. From a height of about 2–3 inches, gently drop each pan 1 time on the counter to get rid of any air bubbles. Place pans in the oven for 25–30 minutes, until a toothpick inserted in the middle comes out clean. Remove from the oven and place the pans on the counter for 5 minutes. Remove the cakes from their baking pans and allow to cool completely on a cooling rack.
To make the frosting, place the remaining butter, powdered sugar and remaining vanilla in a small mixing bowl. Beat on low until the butter and powdered sugar come together in a heavy frosting. Add the cream a bit at a time and then beat for 1–2 minutes, until the frosting is light and fluffy. Set aside.
In a small mixing bowl, add the Cointreau to the jam and mix. Set aside.
When the cakes have cooled completely, place the first layer on a serving dish or a cake stand. Spread the Cointreau and jam mixture over this bottom layer. Place the next layer on top. Use the frosting to cover both the sides and the top of the cake completely. Add the sliced strawberries on top. Reserve more for serving. Slice and serve. Will keep for 1–2 days in the refrigerator.