Make the sugar syrup
In a small, heavy saucepan over medium-high heat, combine the sugar with ½ cup (4 fl oz/125 ml) water and heat, stirring occasionally, until the sugar dissolves, about 3 minutes. Remove from the heat, pour into a heatproof bowl, and stir in the ice cubes. Continue stirring until the sugar syrup is cold, about 1 minute. Discard any unmelted ice. You will have about 1¼ cups (10 fl oz/310 ml) syrup.
Make the granita base
In a food processor, combine the cantaloupe, lemon juice, and sugar syrup. Pulse a few times until the cantaloupe is broken up, and then process until a smooth purée forms, about 1 minute.
Freeze the granita
Pour the cantaloupe mixture into a 9-inch (23-cm) square stainless-steel pan or heavy glass dish. Freeze until the mixture is just frozen, about 1 hour. Using a fork, stir and scrape the granita to break up the ice crystals into clumps with a slushy texture. Return to the freezer and freeze until firm, but not solid, up to 1 hour. Spoon into glasses or bowls and serve.