Heat water and sugar in a small saucepan over medium heat and whisk until sugar is dissolved, about 3 minutes. Remove pan from heat and add sliced ginger rounds. Let steep until slightly cooled, about 30 minutes.
Puree raspberries, lime juice, fresh ginger and salt in a high speed blender or food processor until smooth.
Place a fine mesh strainer over a bowl and press raspberry mixture through with a rubber spatula to separate the liquids; discard solids.
Once simple syrup has cooled, strain over same bowl and stir to combine with the raspberry liquids.
Place raspberry-ginger mixture in a bowl, cover with plastic wrap and refrigerate until cold, about 4 hours or over night.
Pour mixture into ice cream maker and freeze according to manufacturer’s instructions.
I like to let the natural berry flavor shine but you can add up to ½ cup additional sugar to the simple syrup for an even sweeter sorbet. Likewise, the more sugar you add, the smoother the sorbet.