Dissolve the sugar and water in a saucepan on medium heat, stirring constantly until the mixture is clear, about 6 to 8 minutes. Turn the heat to high and cook without stirring until the caramel turns a honeybrown color, about 5 more minutes. Remove from the heat immediately and cool while you prepare the apples.
Peel, core, and quarter the apples. Melt the butter in the skillet. Arrange a fan of apple slices in a circle around the perimeter and fill in the center with the remaining slices. Cover and cook on medium heat for 8 to 10 minutes, until the apples begin to soften. While the apples cook, carefully stir the sour cream into the cooled caramel (it may sputter if the caramel is still very hot). When the apples are becoming tender, sprinkle on the lemon juice and salt and pour the caramel evenly over the apples.
Trim the corners from the pastry to make a rough circle about 10 inches in diameter. Fit the dough over the apples, tucking in the edges around the inside of the pan. Bake for 30 minutes, until the pastry is puffed and golden. Remove from the oven and let stand for 5 minutes. Cover with a plate larger than the skillet and invert very carefully to unmold the tart onto the plate. Serve warm.