Put sugar and 1/3 cup water in a small saucepan and bring to boil over high heat, stirring until sugar is dissolved. Set aside.
Combine blueberries, strawberries, raspberries, and lemon juice in a blender and purée until smooth, about 30 seconds. Add 1/3 cup simple syrup and blend just until combined. (Save remaining syrup for another use, such as sweetening iced tea.)
Transfer purée to popsicle molds (see Notes) and freeze 4 hours. Insert popsicle sticks and freeze an additional 4 to 6 hours, or until frozen solid.
Note: Nutritional analysis is per popsicle.