Place whole grapes in blender or food processor and pulse just until they liquify but the skins do not break down, about 10 seconds. Pour through a fine-mesh strainer into a work bowl, pressing down on skins and seeds with a spoon to release juices; you should have about 2 1/2 cups of purée. Whisk in sugar and salt until dissolved, then taste. If too sweet, add lemon juice 1/8th teaspoon at a time. Chill base in refrigerator until very cold, 2 to 3 hours. Churn in ice cream maker according to manufacturer's instructions. Transfer sorbet to freezer and chill until firm, at least 3 hours.
