The dealership had a look at it and first they though it was a faulty lambda sensor, but then tested a bit more and found that it didn't have any power. They needed to book it in for further testing, but they had some trouble with their IT systems so they reset the error and told me to call them 3 days after the light came on again.
The car has default values for oxygen, so the lambda unit is not crucial and it's harmless to drive without it. I'm going to book the car in next week.
I've sen't the box with loom to Koch, and they should be sending me a new wiring loom as well as testing the box to be sure it works.