probably firewall issue: port 7080 not open to outside.
to confirm this, ssh to your server, run command:
#curl -I 127.0.0.1:7080
if it's ok, then it's the firewall issue.
do you mean you can't access :7080, lsws web admin console?
for install lsws with cPanel, just follow
http://www.litespeedtech.com/support/wiki/doku.php?id=litespeed_wiki:apache:ezcpanel
will be easiest.
assume the file $DOC_ROOT/abc.dat, direct access URL is http://domain.com/abc.dat
the php code is just 1 line:
header("X-LiteSpeed-Location: /abc.dat");