Combine sugar, 1 cup of water and lemon zest in a small saucepan. Bring to a simmer and cook for 10 minutes. Cool.Puree strawberries in a food processor until smooth. Strain the puree through a fine mesh strainer, pressing down on the solids to get all the good juice out.Strain the cooled lemon sugar syrup through a fine mesh strainer.Combine the syrup, the strawberry puree, the lemon juice and the remaining water in a large pitcher and stir. Add ice cubes and serve!