Place the water and sugar in a pan, bring to a boil, and simmer for 4 minutes with the lime zest. Remove from the heat, and allow to cool for a while. Add the lime juice and basil puree. Stir this up and leave to infuse for a while. Pass it through a coarse sieve and pour into a plastic tub or earthenware dish and place in the freezer. Generally, sorbet takes 2 hours to set. Try to stir it around every 30 minutes, if you remember. Serve it in a glass on its own.