Add the plum slices and a quarter cup of water to a medium-sized saucepan. Cook over medium heat with the lid in place, stirring occasionally. Once the fruit is cooked through and softened, set aside and cool.
Blend the plums with a stick blender or food processor until smooth. Push the fruit through a sieve and set aside.
Add sugar, salt, and lemon juice to a medium saucepan along with ¾ cup cold water. Allow the syrup to boil, then reduce the heat and simmer for two minutes. Remove from heat and allow to cool.
Whisk the plum puree into the sugar syrup and refrigerate for at least three hours, preferably overnight.
Churn the sorbet in an ice cream maker according to the manufacturer's instructions. Scoop the dessert into a freezer-proof container and harden for three hours before serving.
