Bring 4 cups of the water to a boil in a kettle or saucepan.
Add the black tea bags, remove from heat, and steep until robust, 5 minutes. Discard the tea bags and let the tea cool to room temperature, 20–30 minutes.
While the tea cools, make the lemonade: In a large pitcher, whisk the lemon juice and granulated sugar with the remaining 3 cups cold water until the sugar is fully dissolved.
Pour the cooled tea into the pitcher with the lemonade and stir gently to combine.
Fill serving glasses with the ice cubes. Divide the Arnold Palmer among the glasses.
Garnish each glass with a lemon slice, if using. Serve immediately, cold.