Put the water and sugar in a small saucepan and heat while stirring until the sugar has dissolved. You can also use the same amount of powdered sugar, this is a little faster. Add the squeezed lemon juice and continue stirring. Let the juice cool down, put it in an ice cube tray and freeze.
When the cubes are frozen, place in a crusher or food processor, crush finely and serve.
Wherever I come from, people like to enjoy the freshly crushed ice cream in the middle of a brioche.