Combine the blackberries, water, and honey in a small saucepan and heat gently over low heat, stirring just until the honey dissolves and the berries release their juice without boiling, then remove from heat, add the lemon zest, cover, and let steep for about 10 minutes before straining through a fine-mesh sieve and cooling completely.
Add the lemon pulp and the mashed blackberries to a large pitcher and gently muddle together just until juices are released and a light, textured base forms, keeping everything loose and avoiding a smooth purée.
Add the fresh lemon juice, about 120 ml of the cooled honey–blackberry syrup, the pinch of fine sea salt, and the ice-cold water, then stir well until fully combined and taste, adjusting with more syrup for sweetness, more water if the flavor feels dense, or a small splash of lemon juice only if the blackberry depth starts to overpower the citrus backbone.
Refrigerate for 1–2 hours until fully cold and integrated.
Fill glasses with ice, pour over the chilled blackberry lemonade, and garnish with lemon slices and fresh blackberries.