In a medium saucepan, combine the sugar and water. Heat over medium heat, stirring until the sugar dissolves completely. Remove from heat and let cool to room temperature.
In a blender, combine the chopped peaches, cooled sugar syrup, lemon juice, and vanilla extract. Blend until smooth.
Pour the peach mixture into a shallow dish and place it in the freezer. Freeze for about 2 hours, stirring every 30 minutes to break up any ice crystals.
After 2 hours, continue to freeze until the sorbet is firm, about 2 more hours.
Before serving, let the sorbet sit at room temperature for about 5 minutes to soften slightly. Scoop into bowls and enjoy!