Find a pitcher that will hold 2 ½ quarts of liquid. (If you don't have a large enough pitcher, you can either scale the ingredients down accordingly, or mix the ingredients in a large bowl and store the extra lemonade in the fridge until you have more room in your pitcher.)

Make thyme simple syrup: Put the sugar in a medium saucepan. Add thyme and ¾ cups cold water, stirring to combine. Heat the mixture over medium-low, stirring occasionally, until the sugar has melted, then remove from heat.

Remove and discard the thyme and allow the sugar syrup to cool to room temperature. (If you're in a hurry, you can speed this process by cooling it in an ice water bath.)

Squeeze the juice from the lemons to make 1 cup. Depending on the size of your lemons, you may not need all of them.

Remove the skin from the peach and cut the peach into chunks. Add the chunks to the pitcher and use a potato masher or fork to mash them into a liquidy pulp. Add the lemon juice, ¾ cup of the simple syrup, 2 quarts of cold water and a very small pinch of salt. Stir to combine.

Taste by pouring a small amount over a single ice cube and swirling to cool it. Add more sugar syrup to the pitcher if needed until it is as sweet as you like it.

When serving, add the ice to the glasses rather than the pitcher so the ice doesn't dilute the lemonade as it sits.