Order the users by the date of their latest post

Put this in your functions.php:

function get_users_ordered_by_post_date($args="") {
    // Prepare arguments
    if (is_string($args) && '' !== $args)
        parse_str($args, $args);
    $asc = (isset($args['order']) && 'ASC' === strtoupper($args['order']));
    unset($args['orderby']);
    unset($args['order']);

    // Get ALL users
    $users = get_users($args);
    $post_dates = array();
    if ($users) {
        // For EACH user ...
        foreach ($users as $user) {
            $ID = $user->ID;

            // ... get ALL posts (per default sorted by post_date), ...
            $posts = get_posts('author=".$ID);
            $post_dates[$ID] = "';

            // ... then use only the first (= newest) post
            if ($posts) $post_dates[$ID] = $posts[0]->post_date;
        }
    }

    // Sort dates (according to order), ...
    if (! $asc)
        arsort($post_dates);

    // ... then set up user array
    $users = array();
    foreach ($post_dates as $key => $value) {
        // $user = get_userdata($key);
        // $users[] = $user->ID;
        $users[] = get_userdata($key);
    }
    return $users;
}

The above function returns an array of WP_User objects.

// EDIT: the function now supports an args parameter (either string or array). The output is ordered with respect to order=DESC and order=ASC. The order_by parameter is remove (we want to order by last post date anyway), all other parameters are passed to get_users.

Now, you can use the function like so:

get_users_ordered_by_post_date();

or

get_users_ordered_by_post_date('role=author');

or

// order by OLDEST post first
get_users_ordered_by_post_date('role=administrator&order=ASC');