$(menu).sortable('toArray');

["", "", "sortable", "", "sortable", "", "sortable", "", "", "sortable", ""]

<ul id="sortable">
<li data-item-id="1"><span>Item 1</span></li>
    <ul id="child-sortable" data-parent-id="1">
        <li data-item-id="2"><span>Item 2</span></li>
        <li data-item-id="3"><span>Item 3</span></li>
    </ul>
<li data-item-id="4"><span>Item 4</span></li>
</ul>

var data = {
    1:[2,3],
    4:[]
};

$("#sortable").sortable('toArray');