Yes,the most difficult part is always an LMIA.It's process is hard and fees are high and there are limit to how much employer can hire Foreign Worker. My LMIA /My employers LMIA has been rejected 3 times. I also had many opportunities when I had employers willing to hire me,who had already got approved LMIA but for some reason I refused it and have been regretting it since 3 months. It's hard,it seems likely impossible but it's possible with little extra effort. Better than paying $25000. U.S to agents/recruiter for job in Canada.Yes, this is what I have experienced.
Not only in Canadian companies also outsider.
Still it seems like LIMA is impossible.