CKEditor 4 stylesSet - apply class for elements with specific parent

I have CKEditor 4.13.1 installed. I would like to create a custom style in stylesSet for adding a CSS class to the items of a specific UL.

CKEDITOR.stylesSet.add('new_style', [
  { name: `Items of a specific ul`, element: 'ul.specific > li', attributes: { class: 'some-class' } }
]);

There would be more of such rules, and since li.some-class has a meaning only in the context of ul.specific, I would like these items in the dropdown list of the CKEditor to be visible only when the cursor stays at a child LI of ul.specific, and not for any LI.

Is there a way to achieve this?