In older versions of Joomla I used this code
$span = $item->note;
if (!(empty($span))) {
$span = '<span class="lidesc">'.$span.'</span>';
} else {
$span = null;
}
which I added in menu module files and adding
<?php echo $span; ?>
in switch operator.
But in the latest version of joomla I can't understand how to 'echo' menu item description.
I found a solution. In menu module files need to add code to $linktype .
$linktype = $item->title . '<span class="lidesc">' . $item->note .'</span>';