Hello,
MS Word style can be applied to HTML lists setting the customListStyles option as true. On https://www.phpdocx.com/documentation/introduction/html-to-word-PHP you can find the following sample:
$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 subitem.</li>
</ul>';
$docx->embedHTML($html, array('customListStyles' => true));
Note that lists always include a numbering style and can also have a paragraph style; both styles can be applied to the same list. DOCXCustomizer can be very useful for this tasks, and the parseStyles method returns the information about existing styles, maybe you are not applying the correct style name/id.
As this is a very specific task, we recommend you to open a ticket (https://www.phpdocx.com/support) and attach your template. The dev team can generate a custom sample using your template.
Regards.