You can strain out the seeds if you like, but the texture is really good with the seeds. Feel free to use boysenberries, pitted cherries or other fruits instead of whats listed.
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 puree until smooth, about 30 seconds. Add 1/3 cup simple syrup and blend until just combined. (Save remaining syrup for another use, such as sweetening ice tea.)
Transfer puree to popsicle molds and freeze 4 hours. Insert popsicle sticks and freeze an additional 4 to 6 hours, or until frozen solid.