Things are gettung more interesting.
After reinstalling everything from the ground up, eventually I have managed to enable php-fpm.
However, upon switching to unix socket mode, Lighttpd throws the following error:
2012-07-03 22:02:30: (mod_fastcgi.c.2854) fcgi-server re-enabled: unix:/tmp/php5-fpm.sock
2012-07-03 22:02:34: (mod_fastcgi.c.1734) connect failed: Connection refused on unix:/tmp/php5-fpm.sock
2012-07-03 22:02:34: (mod_fastcgi.c.3027) backend died; we'll disable it for 1 seconds and send the request to another backend instead: reconnects: 0 load: 1
2012-07-03 22:02:35: (mod_fastcgi.c.3597) all handlers for /index.php? on .php are down.
I must add that I had to touch /tmp/php5-fpm.sock because it was not automatically created by neither lighttpd nor php-fpm.
root@rtvnwebfpm:~# ls -l /tmp/php5-fpm.sock
-rw-r--r-- 1 www-data www-data 0 Jul 3 21:59 /tmp/php5-fpm.sock
Aghh... my extremely poor sight playing tricks on me. Copied isten = /tmp/php5-fpm.sock instaed of listen = /tmp/php5-fpm.sock
Sorry about that