Fill a large bowl with ice water. Place another bowl inside so it's surrounded on all sides by the ice water. In a medium saucepan, bring water and sugar to a boil. When sugar has dissolved, remove from heat and add lime juice. Pour into bowl sitting in the ice bath to cool lime mixture, about 15 minutes. Pour mixture into a 10 by 12-inch baking dish that's sitting on a sheet tray and put in the freezer. After 1 1/2 hours, remove from freezer and scrape the ice with a fork, being sure to mix the softer center with the more frozen outer edges. Put back into the freezer for another 1 1/2 hours. Before serving, scrape again using the fork.