Prepare the grill for indirect cooking over medium heat (about 350°F).
Grease a 9-inch round cake pan (2 inches high) with the butter. Line the bottom of the pan with a round piece of wax paper. In a medium bowl sift the flour, baking powder, and salt.
In the bowl of a stand mixer with the whisk attachment or using a hand-held mixer, beat the sugar and eggs on high speed until the mixture is tripled in volume and pale yellow in color, 4 to 5 minutes. In a small bowl whisk the milk, oil, and vanilla. Pour the milk mixture into the bowl with the sugar and eggs and beat for 2 minutes more. With the mixer on low speed, add the flour mixture and mix until just combined, scraping down the sides of the bowl. Pour the cake batter into the prepared cake pan and smooth the top with a spatula.
Cook the cake over indirect medium heat, with the lid closed, until a wooden toothpick inserted in the center comes out clean and there is no jiggle in the center of the cake, 35 to 40 minutes, rotating the pan 90 degrees once halfway through cooking time. Remove from the grill and let cool completely on a wire rack. Run a knife around the edge of the cake, making sure to reach down to the bottom of the pan. Invert the cake out of the pan onto another wire rack or board and discard the paper. Invert the cake again onto a serving platter.
In a medium bowl mix the cherries, 2 tablespoons of the sugar, and the lemon juice. Let stand at room temperature for 5 to 10 minutes. Meanwhile, whip the cream with the remaining 2 tablespoons of sugar to stiff peaks. Cut the cake and serve with the cherries and whipped cream on top.