To make the syrup, in a small pot, combine water and sugar. Cook over medium-high heat until the sugar has melted and the syrup starts to boil, stirring occassionally. Remove from heat to cool.
In another small pot, combine the tea leaves and 3 cup of water. Bring to a boil over high heat. Once it starts to boil, reduce heat to low and cook for 5 minutes. Strain the tea through a sieve to a large glass measuring cup or a medium bowl. Discard the tea leaves. Let the tea cool at room temperature for at least 30 minutes.
Add the lemon slices into the tea. Using a spoon, poke each lemon slices (the flesh part) a few times to release the flavors. Add all the syrup. Stir and taste. If there isn't enough lemon flavors, poke the lemon slices a few more times.
Sieve the tea into an easy-pour container. Fill the popsicle molds by leaving 1/8-inch space on top. If using molds that contain sticks or hold wooden ones in place, put on lids and freeze. If using open cup molds, freeze until beginning to set, about 1½ hours, then insert the sticks and put back in freezer.
After about 5 hours, popsicles are ready. If the popsicles are stuck in the molds, dip the molds in warm water for 10 seconds or so. Remove molds and serve.