My post grad work permit is about to expire but it's unlikely I will receive the CEC file number within two months. So I am considering a post grad LMO. can some one please tell me how long it takes to apply and how much it approximately cost?
First, you can't apply for LMO. your employer can only apply for your LMO.
Second, your new work permit application would be open only till a certain time while CIC will be waiting for your LMO decision, after which it would be denied. If that happens, your would loose your legal status in the country and you would have to apply for status restoration within 90 days of refusal of work permit. restoration process can take up to 3-4 months and during this period you can't work in Canada. So it would be a very unfortunate situation for you. Try to avoid this as much as you can.
LMO processing times vary a lot and can take anywhere from 1 month to upto 6 months.