In a large bowl stir together flour, baking soda, salt, cinnamon and sugars. Add butter, one egg and vanilla; blend with electric mixer on low speed.
Increase speed to medium and beat for 2 minutes. Scrape down sides of bowl. And remaining eggs, one at a time, beating 30 seconds after each addition. Add carrots, pineapple, raisins and walnuts. Blend on low until thoroughly combined. Pour batter into prepared pans and smooth the surface with a rubber spatula. Bake in center of oven for 60-70 minutes. Toothpick inserted into center should come out clean. Cool in pans for 10 minutes. Then invert cakes on rack and cool to room temperature.
TO PREPARE ICING: In a medium bowl with electic mixer on medium speed, beat cream cheese and butter until smooth; add lemon juice and vanilla; beat until combined. Add sugar gradually, mixing on low until smooth.
TO ICE THE CARROT CAKE: Place one layer on a cake platter, and with a metal spatula spread icing over the top to form a thin filling. Place second layer over the first, rounded side up. Coat the top and sides of the cake evenly with remaining icing. Refrigerate 1 hour to set icing.