In a blender or food processor, purée strawberries; pour into a pitcher and set aside. In a small saucepan, mix 2 cups water and 1 cup sugar; bring to a boil. Reduce heat; simmer until sugar is completely dissolved. Remove mixture from heat; chill completely in the refrigerator (about 1 hr.). Stir in zest and lemon juice; pour into the pitcher with the strawberry purée. Add 2 cups water; stir well. Serve over ice with a sprig of fresh mint and a strawberry for garnish.