Clean raspberries. Freeze fruit in an even layer on a large baking sheet.
In a small saucepan, simmer sugar and water, until the sugar dissolves; allow simple syrup to cool.
Pulse frozen raspberries and lime juice in a food processor until coarsely chopped. With machine running, pour in the cooled simple syrup; Process until the mixture is smooth.
Press the raspberry mixture through a fine mesh sieve to remove most of the seeds.
Transfer to an airtight container, and freeze until firm OR pour the mixture into an ice cream maker and freeze according to manufacturer’s instructions. The sorbet will be somewhat soft after churning, but will firm up after freezing.