With a vegetable peeler, pare green part of peel from four limes. Put peel and sugar in a food processor and whirl until peel is very finely chopped.
Cut limes in half; ream enough juice to make 1 cup. Add to sugar mixture and whirl until sugar is melted. Cover mixture and chill until cold, about 45 minutes.
Pour lime-sugar mixture through a fine strainer into an ice cream maker (1-qt. or larger capacity), then pour 3 cups ice water through strainer into maker; add orange-flavor liqueur. Freeze according to manufacturer's directions until dasher is hard to turn or machine stops, about 25 minutes.
Serve softly frozen, or cover and freeze to store longer. If frozen hard, let stand at room temperature until soft enough to scoop, 10 to 20 minutes. If desired, cut one lime into thin slices (discard ends) and garnish portions with slices.
Nutritional analysis per 1/2 cup.