In a food processor or blender, puree strawberries, 1 teaspoon lime juice, 2 tablespoons sugar, and 1 tablespoon water until completely smooth, scraping down sides as necessary. Transfer to a bowl and set aside.
Wipe food processor clean. Add blueberries, 1 teaspoon lime juice, 2 tablespoons sugar, and 1 tablespoon water and puree until completely smooth, scraping down sides as necessary. Transfer to a bowl and set aside.
Fill 8-9 popsicle molds 1/3 full of strawberry puree. Place in freezer and allow to freeze 1 hour.
Remove popsicles from freezer and spoon Greek yogurt evenly over strawberry layer filling another 1/3 full. Freeze an additional 1 hour.
Remove popsicles from freezer and spoon blueberry puree evenly over yogurt layer filling another 1/3 full. Freeze popsicles 6 hours until solid. Enjoy!