Add the tea bags to the water; steep for 10 minutes. Remove and discard the tea bags.
In a large pitcher, combine the tea, lemon juice, simple syrup and vodka. Stir until well combined.
Serve over ice, garnished with mint leaves and lemon slices.
Bring the water and sugar to a boil in a small saucepan; cook about 10 minutes. Add the mint and let steep for 5 minutes. Strain and cool. Use immediately or store, covered, in a refrigerator.