From the comments I see some confusion over terms like connection, SSL session or handshake. Maybe it will help to clarify these terms:

• Connection: this can be either the TCP connection or the SSL connection (HTTPS) on top of the TCP connection. There might be multiple HTTP requests inside same connection, which is called persistent HTTP connections or keep alive. Keep alive is controlled by conn_cache or keep_alive settings from LWP::UserAgent. My understanding of LWP::UserAgent is, that keep_alive is disabled by default and I cannot see that SOAP::Lite enables it.
• SSL session: An SSL session starts with a full SSL handshake, e.g. negotiating of ciphers, validation of certificate etc. A single SSL session can span multiple TCP/SSL connections, i.e. server and client can cache session information so that the session can be resumed on the next TCP/SSL connection. If you want to get this behavior on the client site with IO::Socket::SSL (which is the underlying class used for HTTPS) you explicitly need to enable it by using session_cache.
• Handshake: In SSL context this refers to the SSL handshake. There might be a full SSL handshake at the beginning of an SSL session and there might be a shortened SSL handshake if a session gets resumed. Also, inside an established SSL session there can be renegotiations which again do SSL handshakes. In HTTP context handshake would probably refer to the pair of HTTP request and HTTP response, but I've seen it rarely used in this context.

Which leads to the question, what you actually want:

• Do you want to make sure that no SSL resumption is done? This should be the default.
• Do you want to disable keep-alive, e.g. have only a single HTTP request per TCP/SSL connection? From my understanding this would be the default too.