MySQL query missing date

I have 2 tables one contains users and their data, the other contains payment transactions which are done but not limited to once per month. I'd like to query users who have not paid at least once. My table users table looks like so.

idu     fname   lname
1       John    Doe
2       Jane    Doe
3       Mary    Jane
4       John    Rancho

My payments table looks like so

payment_id  uid payment_date
1               2       2012-01-07 08:00:00
2               3       2013-01-12 08:00:00
3               1       2012-02-01 08:00:00
4               2       2012-02-07 08:00:00
5               3       2013-02-12 08:00:00
6               1       2012-03-01 08:00:00
7               2       2015-04-08 08:00:00
8               1       2014-05-31 08:00:00
9               1       2014-07-31 08:00:00

I would love my results to look like the table shown below where unpaid times is the count of months not paid for and is greater than one.

IDU  Name      Unpaid Times
2   Jane Doe    3
3   Mary Jane   4

I did the query in PHP and MySQL in a crappy way though I get desired results. I want to transfer the code to Android and SQLite so an otimised query is highly required. My PHP/MySQL code is shown below. Thanks.

$query = "SELECT idu,fname,lname,date_added,payment_date FROM water_users LEFT JOIN payments ON idu=sold_to GROUP BY (CASE WHEN MONTH(payment_date) IS NULL THEN idu ELSE MONTH(payment_date) END) ORDER BY DATE(payment_date) ASC";    

            $result = $db->RunQueryForResults($query);

            $defaulters = array();

            while ($row = $result->fetch_assoc()) {                   

                $start_date = $row['date_added'];

                while (strtotime($start_date) < strtotime(getCurrentDate())) {
                    $current_month = date("Y-m", strtotime($start_date));
                    $payment_date = date("Y-m", strtotime($row['payment_date']));
                    if ((strtotime($current_month) !== strtotime($payment_date)) && (strtotime($payment_date) <= strtotime($current_month))) {
                        $defaulters[] = array(
                            'idu' => $row['idu'],
                            'name' => $row['fname'] . " " . $row['lname'],
                            'defaulted_month' => date("M Y", strtotime($current_month))
                        );
                    }
                    $start_date = date("Y-m-d H:i:s", strtotime("+30 day", strtotime($start_date)));
                }
            }