For the Cake:

1. Preheat oven to 350°F. Butter and flour 2 (8 inch) round cake pans and set aside.
2. In a medium bowl, combine cake flour and baking powder. Set aside.
3. In the bowl of your mixer, beat butter, sugar, and lemon zest on medium speed for two minutes, until light and fluffy.
4. Add eggs one at a time, beating and scraping the sides of the bowl after each. Add lime juice and mix until smooth.
5. Add flour mixture and milk to the butter mixture alternately, starting and ending with flour. Stir in a few drops of green food coloring. Give the batter a good stir from the bottom, then pour evenly into prepared pans.
6. Bake for about 25 minutes or until tops spring back when lightly touched in the center.
7. Remove from oven and let cool in pans for about 7 minutes before removing to wire racks to cool completely.

For the Frosting:

1. In the bowl of your mixer, beat butter and cream cheese on medium speed until smooth.
2. Add pureed strawberry mixture, beating on low until smooth.
3. Add 5 cups powdered sugar and continue beating on low until JUST mixed.
4. Increase mixer speed to high and beat for one minute. If frosting is too thin, add additional cup of powdered sugar.

Assemble the Cake:

1. Carefully level cooled cakes with a serrated knife, then frost and assemble. Keep uneaten cake stored in the refrigerator.