May be prepared one day ahead.

Preheat oven to 350 degrees. Butter 3 - 9 x 1-1/2 inch round cake pans. Line bottoms with wax paper, butter paper. Cook carrots in large pot of boiling salted water until tender, about 12 minutes. Drain. Puree in food processor, stopping occasionally to scrape down sides of bowl. Transfer to large bowl, cool.

Whisk oil, pineapple, eggs and vanilla into carrot puree. Mix dry ingredients in medium bowl, stir into puree. Mix in nuts. Divide batter among prepared pans. Bake until tester inserted into center comes out clean, about 35 minutes. Cool cakes in pans on racks.

Turn cakes out of pans; peel of wax paper. Place on layer on platter. Spread 3/4 cup frosting over it, top with second cake; spread 3/4 cup frosting over. Top with third cake. Spread remaining frosting over top and sides. Cover with cake dome and refrigerate. Let stand 3 hours at room temperature before serving.

Frosting: With electric mixer, beat cream cheese, butter, lemon juice and vanilla until light and fluffy. Gradually beat in sugar. Chill until firm but spreadable, about 1 hour.

carrots are cooked first.