Rinse 2 of the lime in hot water, pat dry, and thinly slice. Squeeze the juice from the remaining limes. Rinse and dry the mint, then remove the leaves.
Mix the juice with 600 ml (approximately 20 ounces) of water in a jug and chill overnight in the refrigerator. Add the sliced limes and mint leaves. Sweeten to taste with the brown sugar, let infuse briefly, and serve.