From your lsof listing and other parts of your post, you seem to have access to two IP addresses: *.171, and *.172. Is that right?
And are we talking about just running Litespeed here, with no Apache running anywhere, or running both side-by-side, but perhaps on different IP addresses?
My experience is running Apache and Litespeed side by side on one server but serving up web sites off different IP addresses over port 80. That's the sort of setup I was thinking about when I made my config suggestion. Maybe it doesn't match what you want to do.