In a blender, combine the raspberries and the mint. Puree until combined. Add the lemon juice and 3 tablespoons of the simple syrup. Blend to combine. Taste the mixture and add the remaining 1 tablespoon simple syrup if you like. Spoon the mixture into an ice cube tray and freeze for approximately 30 minutes, or until partially frozen. Insert the wooden sticks and return trays to the freezer for another 3 to 5 hours.
In a saucepan, combine water and sugar over medium heat. Bring to a boil, reduce heat and simmer for 5 minutes, until the sugar has dissolved. Take pan off heat and cool the syrup. Any extra cooled syrup can be saved in an airtight container.