1.Place the sugar, water, lemongrass and lime zest into a small saucepan and bring to the boil, stirring to dissolve the sugar.
2.Reduce the heat and simmer for 2-3 minutes then remove and cool completely.
3.Stir in the lime juice then pass the cordial through a fine sieve to remove the lemongrass and lime zest.
4.To serve, fill a glass with ice and add 1 part cordial to 3 parts soda water.
5.Garnish with fresh lime slices and serve.