which version of cPanel are you using? which version of LSWS enterprise?
LiteSpeed redirect access to suspend account to http://domain.name/cgi-sys/suspendedpage.cgi, works the same way as Apache.
It is working fine in our lab environment. Maybe we need to login to take a look if you are using the latest cPanel/Enterprise combination, something special with your setup.
Litespeed was installed only few weeks back. I don't see any .htaccess file in public_html with redirection line. That is what Apache does in order to redirect.
In another server where I have litespeed, the suspension works fine. Still no .htaccess file created in that account too.