To make a simple syrup, combine the sugar with one cup of water. Bring the mixture to a boil and stir until the sugar is dissolved, then cool.
Using a blender or food processor, combine the red velvet apricots with 1 cup of water and a tiny pinch of salt and purée until smooth. Slowly add the cooled simple syrup and stir to combine. Taste the mixture for sweetness. If it's too sweet, add a splash of lemon juice.
Freeze the sorbet in an ice cream maker according to the manufacturer’s instructions. Pack into a freezer container and freeze for at least 1 hour before serving. (The sorbet is best served the day it is made.)