No - it's not enough to submit an LMIA. They have to obtain an approved LMIA. To be honest, it will probably be difficult to get an LMIA approved for a general labour job. To be approved, the employer first needs to advertise the job for at least a month to prove no Canadian could be found for the role. This advertising must be done according to the LMIA advertising requirements (so simply putting something on a free site like craigslist won't do it). The employer must then submit the LMIA application along with a $1K fee and generally wait 2-4 months to see if the LMIA is going to be approved. Not all are.