How to get a count even if there are no results corresponding mysql?

You should LEFT JOIN this table with 1..12 table. Something like this:

SELECT  Months.id AS `month` ,
COUNT(`reports`.date_lm) AS `count`
FROM 
(
  SELECT 1 as ID UNION SELECT 2 as ID UNION  SELECT 3 as ID UNION SELECT 4 as ID 
  UNION  
  SELECT 5 as ID UNION SELECT 6 as ID UNION SELECT 7 as ID UNION SELECT 8 as ID 
  UNION  
  SELECT 9 as ID UNION SELECT 10 as ID UNION SELECT 11 as ID UNION SELECT 12 as ID
) as Months
LEFT JOIN `reports` on Months.id=month(`reports`.date_lm)
                       AND 
                       (status = 'submitted') 
                       AND (date_lm > 2012-08)
GROUP BY Months.id 
ORDER BY Months.id ASC

SQL Fiddle demo

In order to do this, you could create a 'month' table and then use a left outer join between that table and the reports table.

I've never used mysql so apologies if the syntax is slightly off, but this would be the query:

SELECT months.monthNumber,
    count(reports.id) AS `count`
FROM `months` left outer join `reports` on months.monthNumber = month(reports.date_lm) 
WHERE (status = 'submitted') 
AND (date_lm > 2012-08) 
GROUP BY monthNumber
ORDER BY monthNumber ASC

Importantly, the count should be of a column in the reports table, not the months table, or else you would never get a zero.

count(col_name) AS count will give you count 0

For reference you can visit http://www.mysqlperformanceblog.com/2007/04/10/count-vs-countcol/