Take a large glass and fill it with crushed or cubed ice, about three-quarters full, to keep your drink cold without watering it down too quickly.
Brew one green tea bag in about ¾ cup of hot water for 3 to 4 minutes. Remove the bag and let the tea cool completely. Warm tea will melt your ice too quickly, weakening the flavor. You can brew this the night before and store it in the fridge.
Mix ¼ cup of sugar with ¼ cup of water in a small saucepan. Heat on medium-low, stirring until the sugar dissolves (about 2 to 3 minutes). Remove it from the heat and let it cool. You can store any extra syrup in a small jar in the fridge for up to two weeks.
In a cocktail shaker or a large jar with a lid, add the cooled green tea, mango nectar, and lemonade. Add the simple syrup, starting with 1 tablespoon, and taste before adding more. Squeeze in fresh lemon juice.
Put the lid on tightly and shake for about 10-15 seconds to combine the ingredients, giving the drink a light, refreshing texture, like Dunkin's version.
Slowly pour the shaken mixture over the ice. The drink should be a golden-yellow color. Add a lemon slice or a small mango piece on the rim as a garnish. Enjoy it right away for the best flavor.