Halve and squeeze enough lemons to make 1 cup of juice. Put the juice and the lemon halves in a large non-reactive pot.
Add 3 cups water and 2 cups sugar. I used raw sugar that had been in a jar with vanilla pods for a long time, but, use any old kind of sugar.
Bring the water, sugar, lemon juice and lemon halves to a rolling boil while stirring constantly. When you're done, it will look like this:
The boiling will release a great deal of pulp, more juice than even the best squeezer can bring out, and the volatile oils from the peel. This is the step that sets this lemonade apart from all others.
It's also the step that gets discarded when they begin to make lemonade on an industrial and commercial level.
Allow the lemon halves to steep in the resulting syrup while it cools to room temperature.
Once cooled, take the lemon halves out of the syrup and squeeze them again into your pitcher. Use a tea strainer to fish out any seeds, while returning the pulp to the syrup. Pour into a pitcher and cut with more water to your taste. Chill.
Serve in tall glasses with plenty of ice and a slice of fresh lemon for garnish.
After they've consumed an entire pitcher of this nectar your kids will start looking at you with hurt expressions if you ever serve that powdered crap again. Even better, they will start bringing their friends over if they are given a glass of the other stuff while visiting.
Keep a steady supply of this in the fridge during the summer and they'll write songs about you.