In a medium saucepan, bring the strawberries and sugar to a simmer over medium heat. Lower the heat and reduce until thick and jamlike, about 20 minutes.
Using a food processor, puree the berry mixture, then transfer to a bowl. Refrigerate until cold. Stir in the yogurt and lemon juice.
Fold the graham cracker crumbs into the yogurt mixture until half blended. Spoon the mixture into an 8- to 10-count 2.5-ounce ice pop mold and freeze for 30 minutes. Insert ice pop sticks and freeze until solid, at least 4 hours.
