In a small saucepan, combine the sugar and water. Heat gently over medium heat, stirring just until the sugar fully dissolves. Do not boil. Remove from heat and let the syrup cool completely.
Juice the lemons until you have 220–250 ml of fresh lemon juice. Remove any seeds.
In a large pitcher, combine the lemon juice and ⅔ of the prepared simple syrup. Add the ice-cold sparkling water and the fine sea salt. Stir very gently to preserve carbonation and taste. Add the remaining syrup only if needed — this drink should stay crisp and refreshing, not sweet.
Refrigerate briefly if needed, but avoid long chilling once sparkling water is added to preserve bubbles.
Fill glasses with ice, pour over the sparkling lemonade, and garnish with lemon slices.
