1. In a 2-quart saucepan, bring 2 cups water and sugar to a boil, stirring to dissolve. Reduce heat to low and simmer, without stirring, to make a syrup, for 5 minutes.

2. Pour the syrup into a medium bowl, stir in vanilla extract, and transfer to the freezer to let chill for 15 minutes.

3. Purée 1 lb. of the raspberries (about 4 cups) with the syrup in a blender or food processor until smooth. Scrape the purée through a fine sieve into a bowl; discard the seeds. Stir lemon juice into the raspberry purée and pour it into a 2-quart ice cream maker. Freeze according to the manufacturer’s instructions until almost set but still a little slushy, about 25 minutes.

4. Add remaining raspberries (about 1 cup) and continue freezing in the ice cream maker for about 5 minutes. Transfer the sorbet to a plastic container and freeze until completely set, about 1 hour.