In a small saucepan, combine the sugar, 1 cup of water, and a pinch of salt. Heat over medium, stirring until the sugar and salt completely dissolve. Remove from heat and let cool slightly.
In a large pitcher, combine the lime juice and the cooled syrup.
Add the remaining 3 cups of cold water. Taste and adjust as needed. Add a splash more water if it’s too strong or a bit more lemon juice if you like it tangy.
Serve immediately over ice, or chill until ready to serve.