1. Drain apricot syrup into a 1 1/2- to 2-quart pan. Add dried apricots. Grate peel and ream juice from lemon. Add peel and juice to pan. Bring mixture to a boil. Cover and simmer until fruit is plumped, about 10 minutes.
2. If desired, reserve 6 of the nicest-looking dried apricot halves for garnish. Combine remaining cooked fruit with syrup and the canned fruit in a blender or a food processor; smoothly purée.
3. Pour mixture into an automatic ice cream maker and freeze until dasher is hard to turn, about 15 minutes. (Or pour into a 9- by 13-inch metal pan and freeze until firm, about 2 1/2 hours. Break into chunks and whirl in food processor until smooth. Serve at once, or cover and return to freezer until ready to serve, up to 2 weeks.)
4. Scoop apricot sorbet into dishes and top with reserved cooked apricots.