What version of Perl are you running and more specifically, are you using Crypt-SSLeay? The output generated by setting the environment variable seems to be an option of Crypt-SSLeay. In my version of Perl I am not using this module but IO::Socket::SSL which has a debug option as well

So I ran the following tests acivating debug for IO::Socket::SSL and setting SSL_version explicitly. It shows that SSLv3 is not supported.

use strict ;
use warnings ;
use IO::Socket::SSL qw(debug4);
use LWP::UserAgent ;
# my $ua = new LWP::UserAgent( ssl_opts => { verify_hostname => 0, SSL
+_version => 'TLSv1_1' } ); # Runs OK
my $ua = new LWP::UserAgent( ssl_opts => { verify_hostname => 0, SSL_v
+ersion => 'SSLv3' } ); # Fails
my $response = $ua->get( "https://www.google.com/" ) ;
if ( $response->is_success ) {
  # print $response->as_string;
} else {
  print "Something went wrong\n";
}
__END__
DEBUG:
.../IO/Socket/SSL.pm:598: global error: SSL Version SSLv3 not supporte
+d
Something went wrong
[download]

Further reading here: Crypt-SSLeay:

DO YOU NEED Crypt::SSLeay? ^ Starting with version 6.02 of LWP, https support was unbundled into LWP::Protocol::https. This module specifies as one of its prerequisites IO::Socket::SSL which is automatically used by LWP::UserAgent unless this preference is overridden separately. IO::Socket::SSL is a more complete implementation, and, crucially, it allows hostname verification. Crypt::SSLeay does not support this. At this point, Crypt::SSLeay is maintained to support existing software that already depends on it. However, it is possible that your software does not really depend on Crypt::SSLeay, only on the ability of LWP::UserAgent class to communicate with sites over SSL/TLS.