Make the Simple Syrup:
In a medium saucepan, combine sugar and 1 cup water over medium heat.
Stir until sugar completely dissolves and mixture comes to a gentle simmer (about 3-5 minutes).
Remove from heat and let cool completely to room temperature, about 30 minutes.
Prepare the Sorbet Base:
While syrup cools, juice lemons to get 3/4 cup fresh juice. Strain through fine-mesh strainer to remove pulp and seeds.
Zest 2 lemons using microplane or fine grater, avoiding white pith.
In large mixing bowl, combine cooled simple syrup, strained lemon juice, lemon zest, additional 1/4 cup water, and salt.
Whisk mixture until well combined. Add vodka if using (helps prevent sorbet from freezing too hard).
Taste and adjust sweetness or tartness as needed by adding more sugar or lemon juice.
Churn the Sorbet:
Pour mixture into ice cream maker and churn according to manufacturer's instructions, typically 20-25 minutes.
Sorbet is ready when it has a soft-serve consistency and pulls away from sides of bowl.
Transfer sorbet to airtight container and press plastic wrap directly onto surface.
Freeze for at least 4 hours or until firm enough to scoop.
Serving:
Remove from freezer 5-10 minutes before serving to soften slightly.
Scoop into chilled bowls or glasses and serve immediately.
Garnish with fresh lemon zest, mint leaves, or thin lemon slices if desired.