Solved it myself. In /etc/lighttpd/lighttpd.conf , uncomment server.port and set it to a different port (I used 8080). Then look a bit lower, and change the listen on IPv6 port to something else as well (I used 8080 again). After this, I called /etc/init.d/lighttpd restart. The web interface is now running on port 8080, so for me the address was 192.168.1.1:8080.
After this I opened a browser, went to the web interface with the new port, restarted the Acme client, and I got my first Let’s Encrypt certificate.