The biggest problem I had was making the iris visible through the lens. It appeared to me that the lens was darkening the iris so much it was not visible at all. Solution was that I added a gamma modifier to the color of the image that was wired into the shader. So I made the iris much brighter than it was originally supposed to with the side effect that it lost a bit of its blue color. I still wonder if there is a better way to change to transparency of the lens so it does not absorb so much light. Does anybody know?
Here is my result with intermediate steps:
Iris without lens
Iris with lens but without gamma boost
Iris with lens but and gamma boost
Bunny with eyes upgrade