Combine sugar and water in a saucepan and heat over medium, stirring occasionally until the sugar dissolves completely, creating a clear syrup. Once dissolved, remove from heat and let it cool to room temperature.
Meanwhile, juice fresh lemons until you have about half a cup of lemon juice. Grate lemon zest and set aside.
In a mixing bowl, whisk together the cooled syrup, freshly squeezed lemon juice, and lemon zest until well combined. The mixture should be bright and fragrant.
Pour the mixture into your ice cream maker and churn according to the manufacturer's instructions. The mixture will start to thicken and become creamy, with a satisfying swirl forming as it churns.
Once churned to a soft-serve consistency, transfer the sorbet to a shallow container and freeze overnight. This helps it firm up and develop a more scoopable texture.
Before serving, let the sorbet sit at room temperature for 5 minutes to soften slightly. Scoop into glasses or bowls, and enjoy the icy, tangy burst of lemon flavor with a satisfying crunch as it melts on your tongue.