Combine the light brown sugar and water in a medium saucepan and heat gently over low heat, stirring just until the sugar fully dissolves; do not boil. Remove from heat, add the lemon zest, raspberries, strawberries, blueberries, and the fine sea salt, then stir gently, cover, and let steep for 15–20 minutes so the berries release aroma and color without turning jammy or heavy.
Strain the mixture through a fine-mesh sieve into a bowl or measuring jug, pressing very gently only to extract liquid — do not force pulp through or you’ll muddy the drink. Discard the solids and let the syrup cool completely.
Pour the cooled mixed berry citrus syrup into a large pitcher, add the ice-cold water, and stir gently until fully combined and clean.
Refrigerate for 1–2 hours until fully cold and flavors are integrated.
Fill glasses with ice, pour over the mixed berry citrus drink, and garnish with lemon slices and fresh berries.