You might be interested to know that NginX can even embed Lua internally as a scripting language in the configuration[1].
As for your goals of connecting NginX to serve your Lua project, well that's quite simple really. Unlike Apache or Lighttpd, NginX is not an application server. NginX is only a reverse proxying HTTP server that speaks HTTP, FastCGI, and UWSGI. To connect your Lua application to NginX, your Lua application will either need to speak HTTP, FastCGI, or UWSGI. I don't know anything about Lua so I can't really help you figure out which is best, but in terms of setting up with NginX, it mostly just changes which flavor of pass you will use.
As for your goals of connecting NginX to serve your Lua project, well that's quite simple really. Unlike Apache or Lighttpd, NginX is not an application server. NginX is only a reverse proxying HTTP server that speaks HTTP, FastCGI, and UWSGI. To connect your Lua application to NginX, your Lua application will either need to speak HTTP, FastCGI, or UWSGI. I don't know anything about Lua so I can't really help you figure out which is best, but in terms of setting up with NginX, it mostly just changes which flavor of pass you will use.
[1]- http://wiki.nginx.org/HttpLuaModule