First you will need to show some basic code, and how you want to setup an address loop. MIME::Lite is meant for convenience not flexibility. MIME::Lite integrates easily with Net::SMTP, as the example in the link showed. You might be better off doing a small rewrite, to use the features of Net::SMTP. All you need to do is compose your MIME::Lite message and add as as_string to the Net::SMTP object. Untested pseudo code to show the idea:

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

#login once
my $smtp = Net::SMTP_auth -> new( 'zentara.zentara.net' );
$smtp -> auth( 'LOGIN', 'z', 'ztest' );

###### put your loop here #########
foreach my $addr ( @addresses){
 
#compose your message as_string
#you can have a very complex MIME::Lite mail here
my $msg = MIME::Lite -> new ( 
  From  => 'z@zentara.zentara.net',
  TO    => $addr, 
  Subject  => 'Testing Text Message',
  Data     => 'How\'s it going.' );

$smtp->mail('z@zentara.zentara.net');
$smtp->to($addr);
$smtp -> data();
$smtp -> datasend( $msg->as_string() );
$smtp -> dataend();

 }
############################

## quit when finished loop
$smtp -> quit;
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