Preheat oven to 350°F. Line muffin tins with paper liners.
In a large bowl or mixer, beat eggs. Add sugar gradually and beat well. Add oil and beat.
In a medium bowl, mix flour, baking powder, baking soda, cinnamon and salt.
Alternate adding carrots and flour to the egg mixture until just mixed.
Spoon cupcake batter into paper liners until ¾ full.
Bake for 20 minutes or until a toothpick inserted in the center of a cupcake comes out clean.
Transfer to a wire rack and allow to cool completely.
To make icing, beat together the cream cheese and butter until very smooth and creamy. Gradually beat in the icing sugar until smooth. Beat in vanilla and lemon juice. With a knife, spread cream cheese icing on top of each cupcake.
Recipe by Life at Cloverhill at https://lifeatcloverhill.com/2010/04/carrot-cake-cupcakes.html