Heat oven to 350°F. Prepare a 9-inch round baking dish by buttering it.
Whisk flour, baking powder, and salt together in a medium bowl.
In the bowl of a mixer, cream butter and 1 cup of sugar together until fluffy and light in color. Add the eggs, one at a time, scraping down the bowl as needed.
Add the dry ingredients, mixing until combined.
Spoon the batter into the prepared baking dish and smooth the top. Arrange the plums, skin side up, over the top of the batter. Sprinkle the top with lemon juice, then cinnamon, then 1-2 Tablespoons of sugar depending on how sweet the plums are.
Bake until the cake is golden and a toothpick inserted in the middle comes out free of batter, about 45-60 minutes. If it is getting too brown, but is still not set in the middle, place a piece of foil on top without tightening it down around the baking dish.
Cool on a rack. When it is at least at room temperature, (or even the next day when the juices are all soaked back into the batter!), cut into wedges and enjoy!