Using lwp to access ssl is documented here: lwpcook#HTTPS. The only thing that I can see from looking at your code is the website listed doesn't actually exist as an ssl server. Just use the example listed in the docs, and you'll get better error messages and hopefully be able to debug your problem:

use LWP::UserAgent;

my $ua = LWP::UserAgent->new;
my $req = HTTP::Request->new(GET => 'https://encrypted.google.com/');
my $res = $ua->request($req);
if ($res->is_success) {
  print $res->as_string;
}
else {
  print "Failed: ", $res->status_line, "\n";
}
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