How to use a tpl.php file for a theme function
Create a template file lt-unified-login.tpl.php in your theme directory and put this function inside template.php to override theme_lt_unified_login_page &amp; return the HTML output of lt-unified-login.tpl.php.

function YOURTHEME_lt_unified_login_page($variables) {
  $template = drupal_get_path('theme', 'YOURTHEME').'/lt-unified-login.tpl.php';
  return theme_render_template($template, $variables);
}