Toss together blackberries, sugar, and lemon juice. Line baking sheet with parchment paper. Place puff pastry squares on baking sheet. Add a heaping 1 Tbsp of honey cream cheese in the center of each puff pastry square. Spread cream cheese, leaving about 1/2-inch border around the puff pastry square. Fold in about 1/4-inch of puff pastry all around the square. Add blackberries over cream cheese. Gently oil the exposed edges of puff pastry.