In a blender, add the blackberries and 2 cups of the Greek yogurt. Blend until smooth, about 30 seconds if using a high speed blender. Set aside.
In a medium-size bowl, whisk lemon juice and 1 ½ cups of the Greek yogurt.
Layer the popsicles as follows: To the molds add 2 tablespoons blackberry mixture, 1 tablespoon lemon juice mixture, repeat.
Gently tap the molds to remove any air bubbles, then insert the popsicle sticks and the top cover of the mold.
Freeze for at least 5 hours, or overnight is better.
To remove the frozen popsicles from the molds, run the molds through warm water for about 10 seconds or allow it to sit at room temperature for about 5 minutes before removing from the mold.