Combine sugar and lemon juice in a Cuisinart® MultiClad 1½-quart Saucepan; bring to a boil. Reduce heat and simmer until sugar is completely melted. Let cool, then refrigerate for 8 hours before using.
Stir yogurt and lemon zest into the chilled lemon syrup. Stir until completely homogeneous. Assemble a Cuisinart® Automatic Frozen Yogurt - Ice Cream and Sorbet Maker (be sure the chiller bowl is totally frozen). Turn on the machine; pour the liquid mixture into the freezer bowl and let mix until thickened, about 25 - 30 minutes. Turn the machine OFF. The frozen yogurt will have a soft, creamy texture.
If desired, transfer the frozen yogurt to an airtight container and place in the freezer for about 2 hours until firm. If made ahead, take frozen yogurt out of freezer 10 - 15 minutes before serving.