In a medium saucepan, combine water, beets, cinnamon, star anise, and 1 cup cherries. Bring to a simmer over medium-high heat. Reduce heat to medium to maintain a simmer and cook, stirring occasionally, until beets are tender, 15 to 20 minutes.
Discard cinnamon and star anise. Carefully transfer beet and cherry mixture to a blender. Secure lid on blender, remove center piece to allow steam to escape, and place a clean kitchen towel over opening. Blend, starting at low speed and gradually increasing to high, until completely smooth, about 1 minute. (Use caution when puréeing hot liquids.) Return mixture to saucepan.
Stir in salt, pepper, and remaining 1 cup cherries and bring to a simmer over medium heat, stirring often, until cherries are slightly softened, about 5 minutes.
Transfer to a large heatproof bowl or jug. Let cool slightly at room temperature, about 30 minutes. Place sour cream in a small bowl, and gradually whisk in 1 cup warm soup, stirring until well-combined and no streaks remain. Whisk sour cream mixture back into soup until well blended, then stir in lemon juice. Cover and refrigerate until completely chilled, at least 4 hours or up to 3 days. Serve chilled. Garnish with a swirl of sour cream, if desired.
