Combine the granulated sugar, water, and fine sea salt in a medium saucepan; bring to a simmer over medium heat, stirring until the sugar dissolves, 2–3 minutes.
Pit the sweet cherries, then add them to the pan; cook just until the fruit releases some juices and softens slightly, 2–3 minutes. Remove from the heat and let cool for 10 minutes.
Transfer the mixture to a blender and blend until completely smooth, 30–60 seconds; add the lemon juice and blend to combine.
Strain through a fine-mesh sieve into a bowl, pressing on the solids to extract as much liquid as possible. Cover and chill until very cold, at least 2 hours.
Churn in an ice cream maker until softly frozen and pulling away from the sides, 20–25 minutes.
Pack into a chilled container, press parchment or plastic wrap directly onto the surface, and freeze until firm enough to scoop, 2–3 hours.
Let stand at room temperature for 5 minutes before serving for the best texture.