Preheat oven to 350 degrees.
For crust layer, combine softened butter, eggs, and the cake mix.
Stir until combined and press into a greased 9x13 glass pan. Set aside.
For middle/frosting layer. beat together powdered sugar and butter.
Add lime juice until consistency of thick frosting is reached, if needed add more powdered sugar.
Mix in cream cheese, and food coloring.
Set aside one cup of mixture for frosting.
With remaining mixture, beat in two eggs until fluffy.
Pour new mixture over the crust, and bake for 25-30 minutes or until center is done.
Let bars cool for about 15 minutes before spreading the frosting mixture on top.