Instead of excluding files from the rewrite with regexes you could also use url.rewrite-if-not-file instead of url.rewrite-once.
For example:
$HTTP["host"] =~ "my-domain.com$" {
server.document-root = "/var/www/my-domain.com/public/"
accesslog.filename = "/var/www/my-domain.com/app/storage/logs/lighttpd-access.log"
alias.url = ()
url.redirect = ()
url.rewrite-if-not-file = (
"^/[^\?]*(\?.*)?$" => "index.php/$1"
)
}