Lenin and Lime Gin and Tonic Sorbetto

Pour the water into a saucepan and add the sugar. Place over low heat and bring to a boil, whisking often, until the sugar dissolves. Reduce the heat and let simmer for 5 minutes, continuing to whisk until the liquid turns into a syrup. Pour the syrup into a heatproof bowl and set aside for about 30 minutes, stirring occasionally, until cooled to room temperature. For more rapid chilling, fill a sink halfway with cold water and ice and place the bowl of mixture in it for 20 minutes. Pour the tonic water into a bowl, add the sugar syrup, then cover and refrigerate, ideally overnight, until thoroughly chilled (at least 40 °F). Add the gin, lime juice, and lemon juice to the chilled mixture, then pour into an ice cream machine and churn according to the manufacturer's instructions. When the churning is completed, use a spoon or spatula to scrape the sorbetto into a freezer-proof container with a lid. Freeze until it reaches the correct scooping texture (at least 2-3 hours). Decorate each portion with lime slices and serve.