Bring 4 cups of water to a boil in a large pot. Once boiling, remove from heat and add tea bags. Let steep for 5-7 minutes.
While tea steeps, combine 2 cups of water, sugar, and 3 sliced peaches in a medium saucepan. Bring to a simmer over medium heat, then reduce to low and cook for 10 minutes, occasionally pressing the peaches with a wooden spoon to release their juices.
Remove tea bags and squeeze gently to extract the last flavor notes. Strain the peach mixture through a fine-mesh sieve into the tea, pressing firmly on the solids to extract all the peachy goodness.
Add remaining 2 cups of cold water to the mixture and allow to cool to room temperature. Transfer to a pitcher, add the remaining sliced peach and lemon slices, and refrigerate until thoroughly chilled (at least 2 hours).
Serve over ice with fresh mint and additional peach slices for garnish.