Make the simple syrup by combining the sugar and water in a medium saucepan over medium heat. Stir until the sugar completely dissolves (about 3-4 minutes), then remove from heat and let cool to room temperature.
Zest and juice your limes, being careful to avoid the bitter white pith when zesting. Strain the juice through a fine-mesh sieve to remove any pulp or seeds.
Combine the cooled simple syrup, lime juice, lime zest, vodka (if using), and salt in a blender. Pulse briefly until well mixed but not frothy.
Chill the mixture thoroughly in the refrigerator for at least 2 hours or until completely cold. This step is crucial for the best texture.
Process the mixture in an ice cream maker according to manufacturer’s instructions, usually about 20-25 minutes until it reaches a soft-serve consistency. (No ice cream maker? See Recipe Notes for alternative methods.)
Transfer to a freezer-safe container and freeze for at least 2 hours before serving to achieve a scoopable consistency.
Let the sorbet sit at room temperature for 5 minutes before serving to soften slightly for the perfect texture.