You can host multiple ssl virtual hosts with one litespeed web server without using a reverse proxy. Actually, I think Apache can do that as well, so I am confused a little bit by the reason why you need a squid reverse proxy in front of apache, especially when all the servers are on the same machine. Is that because each Apache instance runs as a different user for each virtual host for security reason?
Please correct me if I was wrong, in your case, squid already decrypts ssl connection and forwards decrypted content to backend apache based on the host header.
Litespeed can do the same as well.