In a small saucepan add the lime juice and sugar. DON'T THROW OUT THE LIMES YOU JUICED. Bring to a rolling simmer over medium low heat, then continue to let it simmer for about 5 more minutes. Stirring occasionally with a spoon until sugar is completely dissolved. Transfer into a heat safe small container and place in the fridge for about 30 minutes to an hour.
Cut the juiced limes into smaller pieces and add it to the pitcher.
Then add the cooled lime syrup, ice, and water. Use a large spoon to mix everything. Add more ice if desired.
Optional: but if you would like to make a lime sugar rim you can add 1 tablespoon (12g) of sugar with the zest of one lime. Mix together. To line the glass use a piece of lime wedge to wet the rim and then dip the glass in it.
Add ice to the glass, along with a few pieces of lime, and fill to the top. If desired, garnish with a lime slice, a sprig of mint, and edible flowers.