I have solved this, - this is purely for others, who experience the same as me. And maybe a support would weigh in, with a theory why this happend, even though the whole thing seemed a bit wierd.
After having upgraded to Catalina, I had two Local By Flywheel-sites running, but they were not responding. They got stuck on ‘Resolving host’ (shown in the bottem left of the screen).
Thinking back, - I think I didn’t stop the virtual machine nor LbF, when I had updated to Catalina, which I regret now.
I tried stopping the site, but the sites got stuck on ‘Exporting DB’. So after giving it 3-5 minutes, I forced quit LbF.
Then I opened Virtualbox and could see that the virtual machine looked like it was running fine. I found this post, which was posted about a year ago. And there are no thorough directions on how to get it back up and running.
This is about the time I started sweating…
Especially because of posts like this one, saying: ‘Just remove everything and install it from scratch’, which by no means is a solution for me. I have about 15 sites.
I tried starting LbF again, and I was unable to start the sites. It simply got stuck saying ‘Starting site’.
More sweat…
Then I tried stopping the virtual machine (in VirtualBox, by right clicking on the machine and stopping/starting it).
… Same result.
I could see that I had VirtualBox version 5.2.x or something like this - but version 6 was out. So I tried updating. After that I could start the sites. Wooh!
… But one site was working fine, while another gave me a Nginx 404-error. I might have tried to open that site too quickly, though. I still confused me, that I saw the Nginx 404-error and not the LbF-502-request-error. But that was one of the sites that was open during the Catalina-upgrade. So I tried stopping the site and starting it again. And then everything worked as was fine.