In a large container, combine 2 quarts hot water and tea. Let steep for 8-10 minutes; remove tea bags.
In a medium bowl, mash 1 cup blackberries, 1 cup raspberries, ¼ cup blueberries; stir in sugar and lemon juice.
Add the berry mixture to the tea.
Let the tea cool to room temperature; refrigerate about 3 hours.
Strain mixture through a fine-mesh sieve into a pitcher; discard solids. Stir in remaining blackberries, raspberries, blueberries, lemon slices, and mint.
Serve tea over ice. Garnish with lemons, berries, and mint, if desired.