I guess my first question is why would you want to put the stock air box back on?
Secondly, if it is mapped it will depend on how it has been mapped as to whether it will run okay with the stock air box on. Was it mapped with the ITG on? Is it a generic map or a custom one. If it is a custom one then it may have been maxed out to accept the ITG intake potential.
The thing I find strange though is that it is telling you that it is running lean and not rich! If it was running too rich I could understand it more due to the restricted airflow. Are you sure there is a filter in the stock box?
Have you tried taking it out for a blast with the stock air box on? Could be adaptation?
Clutching at straws a bit here too, but sure is a weird one.