Hello,
What version of phpdocx are you using? Your username doesn't have any license tied, please send to contact[at]phpdocx.com the username or email of the user that pruchased the license you are using.
Your code is not applying the custom list style correctly. Please check the embedHTML/sample_2.php script included in the package, you need to set the class name:
$latinListOptions = array();
$latinListOptions[0]['type'] = 'lowerLetter';
$latinListOptions[0]['format'] = '%1.';
$latinListOptions[1]['type'] = 'lowerRoman';
$latinListOptions[1]['format'] = '%1.%2.';
$docx->createListStyle('latin', $latinListOptions);
$html = '
<ul class="latin">
<li>First item.</li>
<li>Second item with subitems:
<ul>
<li>First subitem.</li>
<li>Second subitem.</li>
</ul>
</li>
<li>Third item.</li>
</ul>';
$docx->embedHTML($html, array('customListStyles' => true));
Also note that using 'stylesReplacementType' => 'mixPlaceholderStyles' you are requesting to mix placeholder and HTML styles. Please check the stylesReplacementType and the available options, maybe you don't need to use that option.
Regards.