LWP 6 makes hostname verification the default -- so note this from LWP::UserAgent:
If hostname verification is requested, and neither SSL_ca_file nor SSL_ca_path is set, then SSL_ca_file is implied to be the one provided by Mozilla::CA. If the Mozilla::CA module isn't available SSL requests will fail. Either install this module, set up an alternative SSL_ca_file or disable hostname verification.
If you use LWP and want SSL, you need IO::Socket::SSL (recommended) and Mozilla::CA.