Not sure if MIME::Lite supports authentication.

Try Mail::Sender by jenda. It supports authentication to the SMTP server.

$sender->MailMsg({
   smtp    => 'mail.server.com',
   from    => 'somebody@perlmonks.org',
   to      => 'tcf22@perlmonks.org',
   subject => 'Sample',
   msg     => 'Mail Sender Sample',
   auth    => 'NTLM',
   authid  => 'tom',
   authpwd => 'pass'
}) ||  die "$Mail::Sender::Error\n";
[download]

Update: Added Code Sample.