In a small saucepan over low heat, combine the sugar and water to create a simple syrup. Bring to a simmer. Using a wooden spoon, stir the syrup to help the sugar dissolve more quickly, about 3-5 minutes. Remove the saucepan from the heat. Set it aside.
As the water and sugar are heating, wash and dry the lemons. Massage the lemons on a hard surface to soften the pulp.
Juice the lemons using either a juicer or a stand mixer fitted with a paddle attachment. If you use a juicer, slice the lemons in half lengthwise in order to extract more juice. Juice the lemons until you have 1 cup of juice.
If you use a stand mixer, cut your lemons into quarters. Toss the quartered lemons into the bowl of the stand mixer. Place plastic or a splash guard on the bowl. Mix the lemons until the juice has been extracted from them. Pour the lemon juice through a sieve into a small bowl. Discard the lemon seeds and pulp.
Combine the lemon juice and the simple syrup in a pitcher. Pour in cold water to taste -- more can be added later. Adding ice will naturally dilute the lemonade.
Refrigerate for 30 minutes before serving.
Room-temperature lemons help soften the pulp, making it easier to juice.
If the lemonade is too sweet, add a little more lemon juice to it. If the lemonade is sour, add a bit of sugar to it.