In a small saucepan, combine the water and sugar and heat gently, stirring just until the sugar fully dissolves without boiling, then remove from heat, add the lime zest, cover, and let steep for 10–15 minutes until aromatic, strain out the zest, and let the syrup cool completely.
In a large pitcher, add the lime pulp and mash gently with a muddler just until juice is released and light structure forms, keeping texture intact and avoiding a purée.
Add the fresh lime juice, 120 ml of the cooled peel-infused syrup, the pinch of fine sea salt, and the ice-cold water, then stir well to combine and taste, adjusting carefully by adding more syrup for sweetness or more water if the acidity is too sharp, using extra lime juice only if the lime flavor itself feels weak.
Refrigerate for 1–2 hours until fully cold and the flavors are integrated.
Fill glasses with ice, pour over the chilled lime lemonade, and garnish with lime slices and lime peel twists.
