In a large saucepan, bring 4 cups of water to a boil. Stir in sugar until dissolved. Add tea bags and steep the tea for 10 minutes, then discard tea bags. Allow the tea to come to room temperature, then transfer to a large pitcher and set in the refrigerator.

In another saucepan, bring remaining water to a boil. Add the raspberries, reduce heat, then simmer uncovered for 10 minutes. Use a fine-mesh sieve or cheesecloth to strain the raspberry liquid and discard pulp. Add raspberry juice to the tea mixture in the pitcher and stir to combine.

Serve cold over ice with fresh raspberries and lemon slices, if desired.