In a medium bowl, smash all the blackberries with a fork until a lumpy liquid is formed.
In another medium bowl, whisk together the yogurt, sugar, and lemon juice. Stir in the blackberry pulp.
Pour mixture into popsicle molds almost to the top. Sprinkle graham cracker crumbs on the base to fill in the rest.
Freeze for 1 hour, place sticks in the molds, and continue to freeze for at least 5 hours.
To remove pops, run hot water over the outsides of the molds for a few seconds, then gently pull the sticks.
Notes
This popsicle recipe was created using a standard bar-shaped popsicle mold, each holding about 1/3 cup. If you are using a different mold, you might need to adjust the ingredients.