Zest all 4 limes using a microplane or fine grater, being careful to only take the green outer layer and avoid the white pith. Add the sugar in a medium bowl. Add the lime zest and rub the zest into the sugar using your fingers or the back of a spoon for about 2 minutes, until the sugar is fragrant, damp, and slightly green.
Transfer the lime sugar to a small saucepan and add the water.
Stir over medium heat until the sugar fully dissolves and the mixture comes to a gentle simmer. Remove from heat and let the syrup cool to room temperature, about 30 minutes.
Stir in the fresh lime juice and citric acid until the citric acid is fully dissolved.
Strain the syrup through a fine mesh strainer into a clean jar or bottle. Press gently on the zest to extract as much liquid as possible. Use immediately or seal and store in the fridge for up to 2 weeks.