1. Combine first 3 ingredients in a large bowl; stir well. Let stand 30 minutes.
2. Squeeze tomato quarters into a wire-mesh strainer over a 4-cup measuring cup. Place squeezed tomatoes into strainer, and firmly press with back of a spoon, pressing until liquid measures 3 cups. Discard tomato pulp in strainer.
3. Process half of tomato juice and half of watermelon mixture in a blender until smooth. Repeat with remaining tomato juice and watermelon. Stir in lemon juice. Pour mixture into freezer container of a 2 1/2-qt. electric ice-cream maker, and freeze according to manufacturer's instructions. (Instructions and times will vary.) Sprinkle each serving with coarse salt, if desired.