Make the lemon syrup while the granita freezes, and refrigerate; strain before serving. Top with extra berries, if desired.
Using a vegetable peeler, remove strips of rind from lemons; reserve. Juice 1 lemon. Place 1 1/2 tablespoons lemon juice, 1 1/2 cups water, 1 cup sugar, rum, salt, and blackberries in a blender; blend 2 minutes. Strain blackberry mixture through a fine sieve over a 13 x 9-inch glass baking dish, pressing on solids with a spatula until only seeds remain. Discard seeds. Cover and freeze 4 hours or until firm, stirring with a fork every 45 minutes. Remove mixture from freezer; scrape entire mixture with a fork until fluffy.
Combine reserved rind strips, remaining 1/3 cup sugar, and thyme in a medium bowl; muddle 1 minute. Let stand 10 minutes. Add 1/4 cup warm water to rind mixture, stirring with a whisk until sugar dissolves. Strain mixture through a sieve over a bowl; discard solids. Place 1 cup granita in each of 8 dessert glasses; drizzle 1 tablespoon lemon syrup over each serving. Sprinkle evenly with grated lemon rind, if desired.