Preheat oven to 350 degrees. Butter a 9x13 inch pan. Spread apples evenly over the bottom of the pan.
Beat eggs with mixer until thick and light. Combine sugar and oil and add to eggs. Stir together flour, cinnamon, soda and salt. Add to egg mixture and beat in. stir in nuts and vanilla. Batter will be very thick. Spread batter over apples in the pan. Bake at 350 degrees F (175 degrees C) for 1 hour, or until a toothpick inserted into the center comes out clean. Remove from the oven and cool. Spread with Cream Cheese Icing.
Topping: To make Cream Cheese Icing: Beat cream cheese until fluffy. Beat in 1/4 cup melted butter, then beat in confectioners sugar and lemon juice. Spread over cooled cake. Refrigerate.