In a medium saucepan make the lemongrass sugar syrup by heating the sugar, water and lemongrass until the sugar is completely dissolved. Let it simmer for 5 minutes. Remove from heat, cover, and let stand one hour.
In a pitcher (capacity 1 liter/34 oz), squeeze the juice from the lemons. Add a pinch of salt. Strain the lemongrass syrup. Mix well. Add 1 to 2 cups of cold water, depends on the desired strength. Refrigerate for at least 3 hours.