Puree the raspberries until smooth using a blender or food processor.

Strain the puree through a fine-mesh sieve to remove the seeds.

Combine sugar, water, and salt in a medium saucepan and heat over medium heat, stirring until the sugar dissolves.

Bring the sugar mixture to a boil, then reduce the heat and simmer for 5 minutes.

Remove the sugar mixture from the heat and stir in the raspberry puree and lemon juice.

Let the mixture cool to room temperature, then cover and refrigerate for at least 2 hours or overnight.

Pour the mixture into an ice cream maker and churn according to the manufacturer's instructions.

Once the sherbet is frozen and scoopable, transfer it to an airtight container and store in the freezer.