After having screwed up in the first try, here’s how the rest of the repair went.
I borrowed a higher quality screwdriver from a friend who is an optician. This one was perfectly able to do the job, although not being a cross slot (like the screws are).
The lense is right underneath the cover. And under the lense, there is a rubber sealing ring to keep water out (the housing is waterproof up to 60 meters.
New lense and seal ring layed on.
Sealing and lense are not glued, they’re just stacked on the housing and held in place by the cover ring.
So to sum up: If he has a good tiny screwdriver at home, the repair can likely be done by any dumbass on this planet.
And dear gopro people … if one of you should happen to read this: please consider including a higher quality screwdriver or leave it out of the pack at all and lower the price reasonably.