Preheat the oven to 350 degrees F (175 degrees C). Grease an 10-inch springform pan.
Sprinkle prepared plums with lemon juice in a bowl.
Combine flour, butter, sugar, eggs, sour cream, baking powder, salt, and lemon zest in the bowl of a food processor; pulse until blended. Process on low speed until smooth. Pour batter into the prepared springform pan.
Arrange plums, cut-side down, on the batter. They can touch or even overlap; the more plums you can fit, the better the cake. Dust with cinnamon.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 45 to 50 minutes. Cool on a wire rack for 15 to 20 minutes before serving. Run a table knife around the edges to loosen. Invert carefully onto a serving plate. Dust with confectioners' sugar.