Preheat the oven to 350 degrees F (175 degrees C). Butter a 9x13-inch baking pan and spread apples evenly over the bottom.
Beat eggs with a mixer until thick and light. Mix in sugar and oil.
Stir flour, cinnamon, baking soda, and salt together in a bowl; add to the egg mixture and beat until incorporated. Stir in walnuts, raisins, and vanilla extract; batter will be very thick. Spread batter over the apples in the pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 1 hour. Let cool, about 30 minutes.
Meanwhile, beat cream cheese until fluffy. Beat in melted butter. Add confectioners' sugar, lemon zest, and lemon juice; mix until well combined. Spread frosting over the cooled cake.