Combine the Lemonade, sweet tea vodka and peach juice over ice in a small mason jar and stir. Garnish with a lemon slice.
To make the agave simple syrup, combine the agave nectar and 1 cup water in a small saucepan. Bring to a boil and cook, stirring frequently, for 5 to 6 minutes. Remove from the heat and let cool.
Measure out 3/4 cup of the agave simple syrup and add to a large pitcher. Add the lemon juice and 5 cups water to the pitcher and mix well. Taste, adding more of the simple syrup if needed. Refrigerate until chilled. (Reserve any additional agave simple syrup for another use.)