Make a simple syrup by combining the sugar with 1 cup of water in a saucepan. Place over medium heat and heat until the sugar in completely dissolved; swirl the pan occasionally. Let cool.
Once the simple syrup has cooled, puree strawberries in a blender with ½ cup water.
In a large pitcher, combine strawberry puree, simple syrup and lemon juice. If using the vodka, add it to the pitcher and stir to combine.
Add 4-6 cups of cold water. The amount of water you use will depend on your taste, so add as little or as much as you want to achieve your perfect sweet/tart balance.
Serve over ice. If desired, garnish with fresh strawberries and lemon slices.