Put lime juice, sugar, and water into a large mason jar, close jar tightly, and shake vigorously for about 60 seconds. Let rest for a minute and then shake again for 60 seconds. If you prefer, you can put the ingredients in a blender and process for a minute to combine. Or you can put the ingredients in a large bowl and whisk vigorously.
Divide mixture between popsicle molds, filling almost to the top, being sure to leave a little space as popsicles will expand as they freeze. Add lime slices to molds if desired. Place cover on top and add popsicle sticks.
Chill in freezer for at least 4 hours, until popsicles are fully frozen.
Gently remove popsicles from mold. If it's difficult to do so, run a little warm water over the molds while you gently jiggle the stick to remove the popsicle.
Store popsicles in freezer, either in plastic wrappers, plastic wrap, or a large Ziplock bag. They should keep for about a month.