What billing software are you using? WHMCS?
Have you checked the httpd.conf generated by cPanel to make sure the configuration for that site is there?
Have you set "Auto reload with configuration changes" for LSWS?
Will a manual restart of LSWS fix it?
There might be compatibility issue between the latest cPanel release and 3.2.4, I will make the 3.3 release package available soon, please give it a try.
I assume that LSWS is configured to use Apache httpd.conf directly, right?