I installed lighttpd in Debian (Jessie), and I wanted CGI to work.
The Welcome/Placeholder page has some information, and part of it is:
CGI scripts are looked for in /usr/lib/cgi-bin, which is where Debian packages will place their scripts. You can enable cgi module by using command “lighty-enable-mod cgi”.
This appears to just not be true. CGI-programs worked perfectly when placed /var/www/html/cgi-bin, but not in /usr/lib/cgi-bin (or /var/www/cgi-bin). This is with default configuration.