How is going ?
I realized lighttpd still binds to ipv6 and maybe nginx will do so too (netstat -nltp).
If so, the two could conflict again at ipv6 level.
If you have not setup your network with ipv6, you can disable ipv6 for lighttpd by hashing out below 1 line in "/etc/lighttpd/lighttpd.conf":
# include_shell "/usr/share/lighttpd/use-ipv6.pl " + server.port
And reload lighttpd to apply new settings:
sudo service lighttpd reload
And check again with:
sudo netstat -nltp
Not sure if you need to disable ipv6 on nginx too but if one is not listening on ipv6 anymore, the other wont conflict (I presume).