Put sugar and ½ cup water in a small saucepan over medium-high heat and bring to a boil. Turn heat to low and gently simmer until sugar completely dissolves and mixture thickens a bit, about 5 minutes. Pour simple syrup in separate bowl and put in fridge to cool.
Put lemon juice in an ice-filled pitcher.
In a separate medium bowl, mash raspberries with a fork or potato masher. Alternatively, you can puree them in a blender or food processor. Push the mixture through a fine mesh sieve to extract the juice into the pitcher with the lemon juice.
Add remaining 1 ½ cups cold water, ½ the simple syrup, and vodka to the pitcher. Stir with a wooden spoon and taste. Add more simple syrup in if desired.
Pour lemonade into ice-filled glasses, garnish with a lemon slice, and enjoy.