Have you created /var/www/logs/ directory? See if you get logs there
Personally I am using something as follows (simple and easy to follow)
Code:
$HTTP["host"] == "domain1.com" {
server.document-root = "/var/www/domain1.com"
server.errorlog = "/var/log/lighttpd/domain1.com/error.log"
accesslog.filename = "/var/log/lighttpd/domain1.com/access.log"
}
$HTTP["host"] == "domain2.com" {
server.document-root = "/var/www/domain2.com"
server.errorlog = "/var/log/lighttpd/domain2.com/error.log"
accesslog.filename = "/var/log/lighttpd/domain2.com/access.log"
}