In a 9- by 13-inch pan, stir pomegranate juice, orange juice, lemon juice, and sugar. Cover airtight.
Freeze mixture until solid, 3 to 4 hours. Break frozen mixture into chunks. Beat with a mixer just until pieces are pea-size. Return granita to pan and freeze, covered airtight, until firm, at least 3 hours or up to 2 days.
Meanwhile, using a zester or grater, cut about 1 tablespoon peel from orange in long, thin shreds.
With a sharp knife, cut remaining peel and membrane from orange. Hold fruit over a bowl and cut between membrane and fruit to release segments into bowl.
Spoon equal portions granita into chilled stemmed glasses or small bowls, sprinkle each with 1 tablespoon pomegranate seeds, and garnish with orange segments and orange peel.