Inserting mysql database results into a multidimensional array in php

Hi Im trying to build a dynamic navigation menu similar on how wordpress does it or so I think but my problem is that my script retrieves only 1 value from my database. What I was trying to accomplish here is to fetch all menu data in my database and store them in a multidimensional array

My database structure looks like this:

Here is how I retrieve the data

global $db;
    $sql = "SELECT * FROM lm_menu";
    $res = $db->prepare($sql);
    $res->execute();
    $result = $res->fetchAll();
    foreach ($result as $opt_h):
              $nav = array(
        array(
            'id' => $opt_h['id'],
            'name' => $opt_h['name'],
            'link' => $opt_h['ref'],
            'parent' => $opt_h['parent']
        )
    );
    endforeach;

And this is the function that reads the array

    function GenerateMenu($nav)
{
    $html = '';
    $html = '<ul class="nav navbar-nav">';
    foreach($nav as $page)
    {
        $html .= '<li>';
        $html .= '<a href="' . $page['link'] . '">' . $page['name'] . '</a>';
        $html .= GenerateNavHTML($page['sub']);
        $html .= '</li>';
    }
    $html .='</ul>';
    return $html;
}

I tried looking for an answer from google but found no luck I saw an article from SO but I didn't tried it because on that article it uses a mysql_* functions while I use PDO functions. Please Help me guys on this one