Your partner cannot apply for the work permit until the employer actually gets the LMIA. The LMIA application is to make sure no canadian wants or can do the job. This involves advertising the job. If the application is successful, THEN they can apply for the work permit.
The fact that the immigration lawyer is asking your partner to lie in order to get a job, is very unsettling and leads me to to question the lawyers validity. If you partner get's caught, he will be banned from Canada for misrepresentation (doesn't matter if the lawyer fills this in or your partner., possibly for five years.