Add all ingredients to a blender and blend on high for about 1 minute or until everything is blended thoroughly. There will be some small chunks of lime rind, which is normal.
Place a fine strainer over a bowl and pour about half of the mix through the strainer. Use a spoon to push the liquid all the way through the strainer. When most of the liquid is through, discard remaining pulp/rind/ice in trash. Pour remaining blender mix through strainer and repeat process of pushing liquid through.
Pour liquid limeade that is in the bowl into a carafe bottle or directly over ice and serve.Can be refrigerated, but be sure to shake well before serving. Optional alcoholic version: Use less or no water and add vodka to your liking. Sugar-free version: Substitute sweetened condensed milk for sugar-free sweetened condensed milk, and substitute white sugar for 2 packets of stevia.