Although lighttpd is not a first class citizen with regard to Nextcloud support, it works very well, as a rule. However, the update to Nextcloud 21 has caused a warning under Settings,Overview that seems to have caused a lot of confusion, whether people are running the fully-supported Apache or Nginx or not. One such discussion, Nextcloud 21 nodeinfo and webfinger, describes the issue, "Your web server is not set up correctly to resolve '/.well-known/webfinger'" and "Your web server is not set up correctly to resolve '/.well-known/nodeinfo'".
While I do not believe these settings are necessary as long as one does not run certain apps, such as the social app, (I may be wrong about that) it is possible to resolve the problem, with the virtual host configuration for Lighttpd as set out below. Where I have FQDN_OF_SERVER and File_Location_of_Server, edit with your own details.
I'm having bizarre trouble ("501 Not Implemented", whatever that means) adding the vhost text file to this blog post so, while I appreciate it's not great to add an attachment, for the sake of publishing this. I've attached a text file of a working lighttpd config. Here's a screenshot too if understandably you're nervy about pulling down the text file: