To a small saucepan add 1 cup water, 4 mint sprigs, zest of 1 lemon, and sugar. Stir. Heat over medium heat to a simmer. Remove from heat and let steep 15-20 minutes.
Remove the lemon zest and mint from the sugar mixture and set aside.
In a pitcher add the raspberry and using a spoon crush slightly.
Add the lemon juice to the pitcher.
Add the cooled sugar mixture and the remaining 3 cups of water. Stir to mix.
Refrigerate until ready to serve.
Serve over ice with additional raspberries, a mint sprig, and a lemon slice, if desired.