Combine strawberries, lemon juice and sugar in a medium saucepan. Cook over medium heat, stirring, until the sugar is dissolved and the fruit has broken down, 8 to 10 minutes. Transfer the mixture to a bowl and refrigerate, uncovered, until completely cooled, about 30 minutes.

Let frozen yogurt soften for a few minutes at room temperature. Stir with a sturdy flexible spatula until pliable. (If it gets too soft, return to the freezer for a few minutes to firm up slightly.)

Alternate layers of 1 tablespoon each of the frozen yogurt and compote into each of six 3-ounce freezer-pop molds until they're almost full. Using a skewer or chopstick, gently stir to create a swirled pattern. Insert sticks. Freeze until solid, at least 6 hours or up to 1 week.