Make the lemongrass simple syrup: Lightly bruise the lemongrass pieces with a muddler or by making fine cuts with a knife. Add the cut stalks and the sugar to a quart container. In a kettle, heat the water to a boil. Wait about 30 seconds before pouring the hot water over the sugar and lemongrass. Stir until the sugar is dissolved. Allow the lemongrass syrup to cool to room temperature, about 15 minutes.
Make the spiked sun tea: In a large glass pitcher, add the tea bags, gin, water and lemongrass syrup. Squeeze the oils from the lemon rinds into the mixture before dropping them in, then give the drink a quick stir.
Wrap the top of the pitcher with plastic wrap and set the pitcher outside in the sun or on a sunny windowsill, and allow to steep for 2 to 3 hours.
When it's done steeping, remove the tea bags and lemon rinds. Serve the tea in rocks glasses with ice.