Add 1/2 cup of water and all of the sugar to a small saucepan. Place the pan over medium heat, and whisk occasionally until the sugar is completely dissolved.
All the simple syrup to cool to room temperature.
Fill a large glass with ice. Pour in the simple syrup, lemon juice, and remaining 1/2 cup of water. Stir to combine before drinking.
Notes
This lemonade is a little on the sweet side. You can reduce the amount of sugar to 2 tablespoons if desired. My kids like their lemonade sweeter and my mom likes it more tart, to each their own.