Preheat oven to 350 degrees.
Place lentils, orange juice, oil and pineapple with juice in a blender and blend until very smooth, scraping down sides of blender as needed. Pour into a mixing bowl.
Whisk together the flour, baking powder, baking soda, spice and salt. Slowly stir into the wet ingredients.
Stir in the walnuts and carrots.
Pour batter into a well oiled 9 by 13 inch baking pan. Bake for 35 to 40 minutes, until set in center. Let cool to room temperature before frosting.
For frosting, mix in a mixer at medium speed all ingredients in order listed until light and fluffy.