after 2.5 monhts and sending in my lighthouse 3 times, I finally got a lighthouse working.
However, HTC again did not manage to send a lighthouse with the current firmware, I have no idea who or what is working the support centers. I will not updated the firmware, because this started all the troubles.
Considering this trouble and that support questions never got answered about the partly chaotic settings/gui, I would not buy again a HTC Vive.