Combine sugar and 1 cup cold water in a small, heavy-bottomed pot. Bring to a boil over high heat, then immediately remove from the heat. Add the matcha and whisk until the matcha and sugar are dissolved.
Pour the lemon juice and 3 cups cold water into a pitcher. Stir in the matcha simple syrup. Taste and add more sugar or more water as desired. Serve with ice cubes and lemon slices.