I collect exchange plan cookbooks, and in a Joanny Lund cookbook I found a recipe for a lemon-shakeup style lemonade. In a blender or food processor, you grind up 1/4 of lemon, with skin and seeds (with a little water if it doesn't grind up easily). You pour the paste into a pitcher, add water and sugar free drink mix (like Crystal Light) to make 2 quarts of lemonade.
The pulp and pulverized lemon peel/seeds, settle to the bottom (even though I stir or shake before pouring a glass).
I was really skeptical, but this does truly taste like lemon-shakeups at the fair, and it's really good. It does create a sludge in the bottom of the pitcher, but the lemonade is wonderful.
You can also do this with oranges too, but not limes or grapefruit. The peel gets so bitter it's horrendous and gets worse and worse as it sits in the pitcher. You can use the fruit of grapefruit and limes, but not the skin (sometimes I mix a whole lemon with a peeled lime or a few segments of grapefruit).
I like this so much that I found a shortcut. I use the food processor to grind the fruit, and then freeze the paste in ice cube trays (when they're frozen, I put them into a ziploc bag).
Then when I make lemonade or other drink mixes, I add one of the the frozen citrus cubes.
Right now I have lemon cubes, and lemon lime cubes in the freezer (the lime cubes are 1/4 of a whole lemon, 1 lime (peel removed), and a little bit of the lime zest that I grated into the food processor, making sure not to get any of the bitter (white) part of the peel.
Tonight I made cherry limeade using a lemon-lime cube and a tub of Walmart's cherry limeade (half the price of Crystal Light and just as good).