Make a simple syrup: Stir the sugar and water in a saucepan over medium-high heat until the sugar dissolves fully and the mixture comes to a boil. Stir in the salt and set aside.
Process the grapes in a blender until the skins are reduced to mere flecks. Strain through a fine meshed sieve, scraping the purée through the mesh to force every bit of liquid through. Discard the solids left in the strainer.
Add lemon juice and more simple syrup to the grape purée to suit your taste. Bear in mind that freezing dulls our perception of sugar, so a little extra sweetness is called for. Refrigerate extra simple syrup in an airtight container for up to a month.
Freeze the purée in the chilled container. After 30 minutes, use the tines of a fork to scrape the frozen crystals into the center of the dish, breaking up any ice chunks. Continue to freeze, scraping every 30 minutes, until the granita is granular and fully frozen, 3 to 4 hours. Spoon into chilled bowls to serve.
*If your grapes have seeds, blending them would make a bitter granita. Instead, halve and cook them with 1 cup of simple syrup in a saucepan over medium heat, stirring occasionally, until liquidy and their skins soften. Force them through a food mill or a fine meshed strainer. Discard the seeds and skins.
**A 9-X-12-inch metal cake pan, or other container of similar volume, is ideal. 1½- to 2-inch sides work well to contain the ice crystals as they are scraped and fluffed.