WordPress add class to parent element if has submenu

I need to be able to add classes to a parent <li> as well as the child <ul> element in WordPress like so:

<ul>
    <li>Top Level Page</li>
    <li class="NEED-NEW-CLASS-HERE">Top Level Page with Children
        <ul class="AND-HERE">
            <li>Child Page</li>
        </ul>
    </li>
</ul>

I can’t quite seem to grasp the whole walker thing, and do not want to do it via jquery. This seems common enough, but I can’t find a working answer anywhere. Has anyone here seen or done this? Any help and insight would be greatly appreciated.