Place the strawberries, sugar, and water in a small saucepan over medium-high heat, and bring to a boil, stirring occasionally until the sugar has dissolved. Reduce the heat to low, and simmer the syrup for 10-12 minutes, until the strawberries are just starting to fall apart.
Pour the syrup through a strainer, and gently push on the strawberries to release the liquid. Let the syrup cool for about 15 minutes. Refrigerate until cold, about 30 minutes.
Place the strawberry syrup in a pitcher. Add the water and lemon juice and stir to combine. Pour in the vodka, and refrigerate until ready to serve.
Serve over ice, garnished with strawberries and lemon slices.