Special equipment: 15 lollipop sticks, candy thermometer
Fill a half sheet pan with an even 1/2-inch-deep layer of the powdered sugar. Press the back of a mold or shape of your choice (like a tablespoon measuring spoon) firmly into the sugar to create an impression as the mold for your lollipops The impression should be at least 1/4-inch deep. Make sure none of the sheet tray shows through the sugar in your mold, otherwise the lollipops will stick to it. Place a lollipop stick with 1/4-inch of the stick inside the impression. Make a dam with the powdered sugar to close the opening in the mold that the stick made, so no sugar syrup can escape. Repeat the process to make 4 rows of 3 molds each.
Reduce the pomegranate juice in a small saucepot over high heat until it's thick and syrupy and there are about 2 tablespoons left, 2 to 3 minutes. (You will only use half of this, but reducing further will not allow for enough liquid enough to pour.)
Combine the granulated sugar, corn syrup and 1/4 cup water in a heavy-bottomed saucepan over medium-high heat and bring to a boil. Heat until a candy thermometer reads 300 degrees F, 10 to 12 minutes (it will just start to caramelize). Remove from the heat and carefully add 1 tablespoon of the pomegranate juice and the lime zest with a heatproof rubber spatula. Carefully transfer the candy mixture to a liquid measuring cup.
Working carefully but swiftly, pour the mixture into the lollipop molds. Allow the candy to cool and harden at room temperature, 15 to 20 minutes. You may dust off any residual powdered sugar with a pastry brush, but it's not necessary. I love that one side is glossy and one side is coated in sugar, it lends itself to the artisanal nature of the pop.
For flavor variations, use orange juice with ginger or grapefruit juice.