In a saucepan, combine 3 1/2 cups water with the raspberries and sugar over medium-high heat. Bring to a boil, lower the heat and simmer for 5 minutes.
Strain over a bowl and press through; discard the seeds. Let cool. Transfer to a pitcher and stir in the vodka and lemon juice; refrigerate until cold. Stir in the beer. Serve over ice.