mkdir /var/log/lighttpd.access.log
mkdir /var/log/lighttpd.error.log
chown www:www /var/log/lighttpd.access.log
chown www:www /var/log/lighttpd.error.log

http://redmine.lighttpd.net/boards/2/topics/144

mkdir /var/run/lighttpd/
and chown it to the user you configured in lighttpd