First, make the lemonade layer mixture. Heat the lemon juice in a small, microwaveable bowl for around 45 seconds and dissolve all the sugar into it. Pour this mixture into a medium bowl with the yogurt and whisk until smooth. Refrigerate until ready to assemble popsicles.
Make strawberry layer mixture. Place the strawberries, water, and sugar in a medium saucepan and bring to a bowl. Simmer for around five minutes until the strawberries are soft. Pour this mixture and the lemon juice into a food processor and pulse until almost pureed, but not liquefied. (I was feeling lazy and used a potato masher) Chill in the refrigerator until cool, and then whisk the yogurt into the strawberry mixture until well combined.
Assemble the popsicles. Use a teaspoon or tablespoon to carefully spoon alternating layers of lemon and strawberry mixture into your molds. If you typically like your lemonade more sweet than tart, use more strawberry layers than lemon. If you prefer more tart than sweet, use more lemon layers than strawberry. Freeze overnight or at least 4 hours until solid. To unmold, dip molds into warm water and gently pull popsicles out. Serve immediately.