In a cocktail shaker, combine the lime juice, condensed milk, water, tequila, and orange juice.
Line out the glasses on a baking sheet, so it will be easy to transport them to the freezer. Fill each cup 90% of the way with the tequila mixture.
Cut the limes into ¼ inch thick slices. Push a craft spoon through the center of each slice, so that half of the stick pokes out from each side.
Top the mixture with the lime sticks. Make sure the lime is resting directly on top of the tequila mixture.
Freeze for at least 6 hours, or overnight. When ready to remove the popsicles from the Dixie cups, simply snip a small cut in the rim of each cup and peel them away. Sprinkle the tops generously with kosher salt.