Preheat your oven to 350°F. Line a baking sheet with parchment paper.
In a large mixing bowl, cream together the softened butter, powdered sugar, and granulated sugar until light and fluffy, about 3-4 minutes. Add the vanilla extract and mix until combined.
In a separate bowl, whisk together the flour and salt. Gradually add the dry ingredients to the butter mixture, mixing until just combined.
Fold in the black raspberry preserves, lemon zest, and lemon juice until evenly distributed throughout the dough.
Scoop tablespoon-sized portions of dough and roll them into balls. Place them on the prepared baking sheet, spacing them about 2 inches apart. Flatten each ball slightly with the bottom of a glass.
Bake in the preheated oven for 12-15 minutes, or until the edges are lightly golden. Remove from the oven and let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.