I seem to remember talk about this recently, but it eludes me now. So I will mention using Net::SMTP_auth, which works with MIME::LITE. I know it's not exactly addressing the point of your post, but maybe the module author has a reason to keep auth and non-auth separate. ( Maybe because it works as it is? )

#!/usr/bin/perl
use warnings;
use strict;
use MIME::Lite;
use Net::SMTP_auth;

my $Servername = "mail.foobar.com";
my $Port = 587;
my $Username = "z+foobar.com";
my $Password = "foobar-secret";
my $Auth_type = 'LOGIN'; #PLAIN, LOGIN, CRAM-MD5#

my $msg = MIME::Lite->new( 
  From  => 'z@foobar.com',
  TO    => 'zentara@zentara.net', 
  Subject  => 'Testing Text Message with auth',
  Data     => 'How\'s it going. Sent with  Net-SMTP_auth' 
  );

#my $msgbody = $msg->as_string();

#my $smtp = Net::SMTP_auth->new($Servername, Port=> $Port );
my $smtp = Net::SMTP_auth->new($Servername, Port=>$Port, Debug => 1 );
$smtp->auth( $Auth_type, $Username , $Password ); 

$smtp->mail('zentara@zentara.net');
$smtp->to('zentara@zentara.net');

$smtp -> data();
$smtp -> datasend( $msg->as_string() );
$smtp -> dataend();
$smtp -> quit;
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