In a blender, combine the blackberries, sugar, and lemon juice. Blend until smooth.

Strain the mixture through a fine mesh sieve to remove seeds.

In a bowl, whisk together the heavy cream and sweetened condensed milk until well combined.

Layer the blackberry mixture and cream mixture in the popsicle molds, creating a ripple effect.

Insert sticks and freeze for at least 4 hours or until solid.