Preheat oven to 350°F. Butter and flour 9x9x2-inch baking pan. Melt 1 tablespoon butter in heavy medium skillet over medium-high heat. Add apples; sprinkle with 2 tablespoons sugar. Sauté until tender and juices cook away, about 8 minutes. Set aside to cool. Mix raspberries into apples.
Using electric mixer, beat remaining 6 tablespoons butter in medium bowl until fluffy. Beat in remaining 1 cup sugar, then eggs 1 at a time. Beat in lemon juice and vanilla extract. Sift flour, baking powder, salt, and ginger over; beat in. Spread 13/4 cups batter in prepared pan. Sprinkle evenly with fruit. Drop remaining batter evenly over by teaspoonfuls, spacing apart (batter will spread to cover during baking).
Bake cake until tester inserted into center comes out clean and top is golden brown, about 50 minutes. Place cake in pan on rack and cool completely.