In a blender, puree the blackberries until smooth. Strain through a fine mesh sieve to remove seeds, if desired.
In a mixing bowl, beat the softened cream cheese until smooth. Gradually add the powdered sugar and vanilla extract, mixing until well combined.
In another bowl, whip the heavy cream until stiff peaks form. Gently fold the whipped cream into the cream cheese mixture until fully incorporated.
Add the lemon juice and mix well.
In a separate bowl, combine the graham cracker crumbs and melted butter. Mix until the crumbs are evenly coated.
To assemble, layer the graham cracker mixture at the bottom of each popsicle mold, followed by a layer of the cream cheese mixture, then a layer of blackberry puree. Repeat the layers until the molds are full, finishing with the blackberry puree on top.
Insert popsicle sticks and freeze for at least 4 hours or until solid.
To remove the pops, run warm water over the outside of the molds for a few seconds. Gently pull on the popsicle sticks to release.