In a food processor (or blender), add in the strawberries and 1/2 cup of the water. Process until completely smooth and no chunks remain. This may take a couple of minutes. Place a fine mesh sieve over a large bowl and pour the mixture into the sieve. Press down lightly with a spatula so that all of the juices pour out into the bowl (see video for reference). Discard the pulp and seeds that are leftover. Set juice aside.

Make the simple syrup by combining the remaining water and the sugar in a medium saucepan over medium-high heat. Bring to a simmer and cook for a few minutes until the sugar is completely dissolved. Set aside to cool to room temperature.

Once cooled, combine the simple syrup with the strawberry juice and mix to combine. Stir in the lemon juice and vodka (see note about leaving out the vodka). 

Serve and enjoy! Store leftovers in the fridge and enjoy within a few days.