Preheat oven to 350 degrees F. Lightly grease muffin tins or line with papers.
In a large bowl, mix the first ten ingredients together.
Add oil, applesauce, beaten eggs and vanilla. Mix just until evenly moist.
Fold in oats and carrots.
In a bowl, blend cream cheese, sugar and lemon juice together until smooth.
Fill each muffin cup about 1/2 full with the muffin batter.
Spoon approximately 1 tsp. cream cheese mixture into the center of each muffin cup.
Top with remaining batter, so that each muffin cup is about 2/3 full.
Bake 15-17 minutes or until a knife inserted in the center comes out clean.
Cool muffins and pipe cream cheese frosting on top of each one, if desired.