Stir the lemonade, simple syrup, and Pimm's together in a measuring cup with a spout; let sit while you prepare the fruit (helps calm the fizz a bit if you let it settle).
Hull the strawberries and cut each one into four slices. Peel the cucumber, then slice off 12 thin slices (use rest for something else). Peel the mandarin orange and separate the segments; if you see any seeds, pop those out. Choose the 4 prettiest segments, and eat the rest (you won't need them in the ice pops.
Divide the fruit evenly among the popsicle molds. Give the liquid ingredients a little stir, then slowly pour it into the molds, leaving 1/2-inch of headroom (the fizz will expand as it freezes). Freeze for 90 minutes (or until slushy), then add popsicle sticks, pushing and stirring the fruit around a bit to distribute while you're at it.
Freeze for another 4 to 5 hours, or until solid.
To make Minty Simple Syrup, combine 1 cup sugar, 1 cup water, and a small palmful (about 2 leafy sprigs) of fresh mint leaves in a small pot; bring to a boil, stirring until all of the sugar is dissolved. Remove from heat and allow to cool completely. Lift or strain out the mint and pour the syrup into a jar; put a lid on and store in the refrigerator for 2-3 weeks. You can use this the extra to flavor cocktails, iced tea, and lemonade. (yield: about 1 1/2 cups)