How to find the following HTML Element

I have a menu with submenu with a structure like this:

<ul>
  <li>
    <a class="navigation-item">Menu Item 1</a>
    <a class="submenu-toggle" />
    <ul class="submenu">
      <li>
        <a class="navigation-item">Submenu Item 1</a>
      </li>
    </ul>
  </li>
</ul>

I want to add a class to submenu-toggle if Submenu Item 1 is selected. How can I find the submenu-toggle in this case?

closest('li') won’ work, this will only find the li after the submenu. closest('li > .submenu-toggle') doesn’t work either because the .submenu-toggle has to be an ancestor of the submenu item. If I could select the correct li, I could then use find('.submenu-toggle'). But how do I select the correct li?

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