Make the lemon simple syrup. In a small saucepan, combine 1 cup of the water, the sugar, and the lemon zest strips. Bring to a boil, then reduce the heat, cover, and simmer for 5 minutes.
Cool it completely. Remove from the heat, discard the zest strips, and let the syrup come to room temperature before using it.
Juice the lemons. Roll room-temperature lemons firmly on the counter, then squeeze to get 1 cup of juice. Strain out the pulp or leave it in, whichever you prefer.
Stir together in a pitcher. Combine the remaining 3 cups of water, the lemon juice, and the cooled simple syrup.
Taste and adjust. Add water for a milder glass, extra syrup for sweeter, or extra lemon juice for tarter.
Chill and serve. Refrigerate for at least 4 hours. Serve over ice, garnished with lemon slices and fresh mint.