Stir together first 6 ingredients in a large bowl, stirring until well blended.
Pour lime mixture into freezer container of a 4-quart ice-cream maker; freeze according to manufacturer's instructions. Garnish each serving, if desired.
Refreshing Lemon Sherbet: Substitute a large lemon for the lime and fresh lemon juice for lime juice. Proceed as directed. Garnish with fresh mint sprigs, thinly sliced lemon wedges, and lemon rind strips.
This was good, and stands up to its billing as refreshing. Once frozen, it becomes a bit icy, so it is best enjoyed "soft serve" right out of the ice cream maker. Also, the zest gets caught on the dasher in the machine; I might try mixing it in at the end next time. I will try this again, but I will be making a few changes; definitely use full fat half & half (I mixed heavy cream and fat free h&h), add a couple of tablespoons of vodka to keep it soft in the freezer, add 1/4 cup extra sugar.
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