Bring the water and sugar to the boil in a small pan, reduce the heat and simmer for approx. 2 mins. Pour the liquid into a measuring cup, allow to cool a little. Add the cucumber, puree. Add the lime zest and juice, briefly puree. Pour the mixture into a stainless steel bowl, leave to cool, cover and freeze for approx. 5 hrs., scrape the mixture four times with a fork until frozen.
Puree the bananas with all the other ingredients, pour into glasses. Top with the granita, serve immediately.