Preheat the oven to 350 degrees F. Grease a 13 x 9 x 2 rectangular pan. set aside.
Sift together flour, baking powder, baking soda, and salt. In a bowl, combine the oil and sugar. Add eggs, one at a time, beating and mixing. Stir in vanilla. Stir in lemon juice. Add the carrots. mix well. Add the fry ingredients and the crushed pineapple with juice. Mix well. Pour into your prepared pan and bake for 35 minutes or until done. Set aside to cool before frosting.
Cream cheese filing:
In a bowl, beat cream cheese and butter until soft. Add sugar and mix well. Add vanilla and lemon juice and mix well. Continue to mix well until soft and fluffy. Put in refrigerator to chill while cake is cooling. When cake is cooled, frost and enjoy with cold glass of milk.