Zest lemon and lime and place in medium saucepan. Juice lemon and lime and add juice to saucepan, along with water, cinchona bark, citric acid powder, lemongrass, and sugar. Bring to a boil on high heat.
Reduce heat to medium-low and cook for 45 minutes. Remove from heat and let mixture steep for 20 minutes.
Strain mixture through two layers of cheesecloth placed in a fine-mesh sieve. Strain again if there are still particles to be removed. This liquid is the tonic syrup. Place the tonic syrup in a sealable glass container and refrigerate for at least two hours before use.
To make tonic water, combine the syrup with carbonated water, mixing one part syrup to four parts water. Do not combine them in a large batch unless you intend to use all the tonic water at once. Instead, combine syrup and fresh carbonated water for each individual use. The tonic syrup will last for about three weeks.