Mix 2 tablespoons of sugar and 2 tablespoons of water in a small saucepan. Heat on medium until the sugar dissolves, about 1 to 2 minutes. Take it off the heat and let it cool completely. You can make this ahead and store it in the fridge for up to two weeks.
If using fresh mango or pineapple, blend the fruit with a little water, then strain. Pour the mixture through a fine-mesh strainer into a bowl. Press down gently with a spoon to get all the juice. Throwing away the pulp gives you smooth juice.
In a tall pitcher or cocktail shaker, mix 1 cup of mango juice, ½ cup of pineapple juice, ½ cup of cold water, 1 to 2 tablespoons of simple syrup, and 1 teaspoon of fresh lemon juice. Stir or shake gently for 10 to 15 seconds until blended.
Fill a 24-oz glass with ice, using crushed or pellet ice for the best results. This type of ice cools the drink quickly and doesn't melt as fast as large cubes. Pour the juice mixture slowly over the ice until the glass is full. The drink should be bright and golden.
Stir it once with a long spoon. If you like, you can add a slice of mango or pineapple to the rim for decoration.