Heat 1/3 cup of water to 195°F (just below boiling) in a small pot or kettle. Add the black tea bags and steep for exactly 5 minutes to extract the tea's flavor without over-steeping, which would make it bitter. Remove the tea bags and set the brewed tea aside to cool slightly while you prepare the remaining components.
While the tea is still warm, stir in the sugar until fully dissolved, then add the apricot juice and fresh lemon juice. The warmth of the tea will help dissolve the sugar completely and allow the flavors to meld together. I like to taste at this point and adjust the lemon juice if needed—sometimes a little extra brightness really brings out the apricot's natural sweetness.
Pour the tea mixture into a glass filled with ice. The ice will quickly chill the tea to drinking temperature while the tea cools down enough to drink immediately. Stir gently to combine any flavors that may have settled, and serve right away for the best flavor and texture.