Make the simple sugar syrup by mixing 1 cup water and 1⁄2 cup sugar in a small saucepan over low-medium heat. Heat the mixture, stirring constantly, until the sugar dissolves and the liquid becomes clear. Let it cool and refrigerate it in a sealed container.
Make the strawberry-raspberry purée by blending the berries until a thick liquid is formed. Add as little water as necessary to allow the fruit to blend. Repeat the process with the blueberries. Store the purées in sealed containers in the refrigerator.
Mix the juice of 1 lemon, 1⁄4 cup water, 2 Tbsp of simple sugar syrup and 1 to 2 spoonfuls of strawberry-raspberry purée in a martini shaker or a pitcher. (In place of the simple syrup, you can substitute 1 Tbsp sugar.) Add more simple sugar syrup or strawberry-raspberry purée to taste. Repeat the process with the blueberries to make the blueberry lemonade.
Pour the juice into the popsicle molds. Add a few sliced strawberries or raspberries into the molds with the strawberry lemonade and a few frozen blueberries into the molds with the blueberry lemonade.
Place the lids on the popsicle molds and place them in the freezer.
Freeze them for several hours or until the juice is frozen.
Remove them from the freezer and gently pull the popsicles out.
Notes
If you have difficulty removing the popsicles from the molds, run some warm water on the tips of the molds while gently twisting the molds to work the popsicles out of the molds.