The main challenge of LMIA in my experience, is time. It is difficult to convince an employer to wait for the LMIA to be processed ( lets say a month ), to fill in the paperwork and then wait an additional 90 days or more for your COPR. Most employers need somebody within a month or two at most.
I have had a few employers interested but it always falls apart at the LMIA stage. This is after meeting them discussing roles, etcetera. I am fortunate in that my work experience makes me quite employable internationally. But it is very difficult to convince an employer to wait that long.
I guess it is technically not impossible to get an LMIA, but certainly is not easy. I would imagine either knowing somebody willing to file the paperwork and wait ( relative or friend ) or be coming to do such a key role for an employer that they are happy to wait.
I am low 400s in score currently but hoping to increase this with another ECA, if this fails, I lose even more points at my next birthday, so am potentially heading out to work on a temporary work permit in Canada in a couple of months and hoping for either gaining points through a years employment in a years time under CEC, or alternatively being lucky enough for OINP, if they ever start issuing to low 400s.
Certainly try, but it is not going to be easy.