In a medium saucepan, combine the sugar, water, and cubed strawberries. Bring to a gentle simmer over medium heat and cook, stirring occasionally, for 12–15 minutes, until the strawberries are very soft but not breaking down. During the last 5 minutes, add the lemon zest to infuse the syrup with citrus aroma.
Remove from heat and strain through a fine-mesh sieve. Press gently — do not force pulp through the sieve. Discard the strawberry solids and let the syrup cool completely.
While the syrup cools, juice the lemons until you have about 1 to 1¼ cups (240–300 ml) of fresh lemon juice. Remove any seeds.
In a large pitcher, combine the cooled strawberry syrup, lemon juice, and ice-cold water. Add the pinch of fine sea salt to sharpen the fruit flavor. Stir well. If needed, adjust with a small amount of extra syrup or lemon juice — avoid adding plain sugar directly.
Refrigerate for 1–2 hours until fully chilled.
Fill glasses with ice, pour over the strawberry lemonade, and garnish with lemon slices and fresh strawberry slices.