In a large bowl, combine sliced lemon with ¾ cup of sugar. Using a wooden spoon, mash the lemons slices in the sugar to release their juices and the oils in the skin. The sugar will begin to dissolve. Set aside and stir/mash occasionally to continue dissolving the sugar.

In a small saucepan, combine the thyme (intact sprigs, no need to chop) with 2 cups of water and the remaining ¾ cup sugar. Stir to dissolve sugar and bruise the leaves. Bring to a simmer, allowing to simmer for about 5 minutes. Remove from heat and let cool.

Once cool, add the herb syrup to the lemon sugar and stir to combine.

Using a fine mesh strainer, strain the lemon-sugar herb mixture into a large pitcher, pressing on the herbs and lemon solids to release all the liquid. Discard the solids.

Add the lemon juice and cold water to the pitcher and stir well to combine.

Chill well and serve over ice.