Combine berry puree, sugar, lemon juice, and vodka in large bowl. Stir on and off for several minutes until sugar has dissolved. (Or, to speed chilling process in next step, combine ingredients in a metal bowl set over a larger bowl filled with ice water.) Rub finger along bottom of bowl to see if sugar has dissolved.
Pour mixture into small container. Seal and refrigerate until mixture is no more than 40 degrees. (If mixture has been stirred over a bowl of ice water, it may already be cold enough, and this step may be omitted.)
Pour chilled mixture into container of an ice cream machine and churn until frozen.
Scoop frozen sorbet into a container. Seal and transfer container to freezer for several hours to allow sorbet to firm up. (Sorbet can be kept frozen for up to 3 days.).