Stir water, sugar and corn syrup in a large saucepan over medium heat until the sugar dissolves. Add peaches (or nectarines); bring to a simmer. Reduce heat, cover and simmer for 10 minutes.
Pour the fruit-syrup mixture into a blender. Add lime zest, juice and salt; blend until smooth. Pour into a large bowl and refrigerate until cold, 4 hours or overnight.
Freeze the sorbet mixture in an ice cream maker, according to the manufacturer's directions. (Alternatively, pour the mixture into ice cube trays and freeze until solid, about 4 hours. Unmold cubes, place half in a food processor fitted with the chopping blade, and process, scraping the sides as necessary, until fairly smooth but still icy. Repeat with the remaining cubes.)