In a medium saucepan over medium heat, combine blackberries, lemon juice, and a pinch of salt.
Cook until the blackberries have released their juices and softened, about 5 to 7 minutes. Mash slightly.
Let the mixture cool completely, then strain through a fine mesh sieve to remove seeds. Set aside the puree.
In a large bowl, beat the heavy cream with a hand mixer until stiff peaks form.
In a separate large bowl, stir together the condensed milk and vanilla extract.
Fold the whipped cream into the condensed milk mixture until smooth.
Swirl in the blackberry puree, creating a marbled effect.
Pour the mixture into a loaf pan, cover, and freeze for at least 6 hours or overnight.