Make a simple syrup: In a small saucepan over medium heat, stir the sugar and water until the sugar dissolves and the syrup is clear, 3 to 5 minutes. Remove from heat and cool.
Blend: Add strawberries, cooled syrup, lemon juice, salt, and vodka (if using) to a blender. Blend until completely smooth.
Optional: For the silkiest texture, strain the puree through a fine-mesh sieve to remove seeds.
Chill the mixture in the refrigerator until cold, about 60 minutes.
Freeze: Churn in an ice cream maker according to the manufacturer’s instructions until thick and slushy, then transfer to a container and freeze until firm. No machine method: Pour into a shallow metal pan and freeze, stirring with a fork every 30 minutes until scoopable.
Notes
Sweetness will vary with your berries. Start with the listed sugar and add more syrup or a squeeze of lemon to balance. For a softer scoop straight from the freezer, include the vodka or replace 2 tablespoons of water with light corn syrup.