Cream 1/2 cup butter or margarine and 1 cup sugar. Mix in carrots, potatoes, and raisins. Sift flour, baking soda, salt, and spices together; mix into the creamed mixture. Stir in apples.

Fill cans 2/3 full with pudding mixture. Cover with foil.

Place cans in a roasting pan with 2 to 3 inches of water. Steam at 300 degrees F (150 degrees C) for 2 1/2 to 3 hours.

Stir together 1/2 cup sugar and cornstarch. Combine mixture with water in a saucepan. Cook and stir over low heat until thick. Stir in 2 tablespoons butter or margarine and lemon juice. Serve warm over pudding.