I heard that the lowest CRS scored candidate was 488 points in June of 2015. In the month of June 2015, there were two draws, one with 482 (on 12-Jun-2016) and another with 469 (on 26-Jun-2016) as CRS cut-off. Check out yourself here.
Does this mean that this person did not have LMIA? Any applicant who gets LMIA (or PNP) can claim additional 600 points (so overall CRS will definitely be 600+). Now you can make inferences.
Is it possible to apply without LMIA 600 points? Yes. Check out this 'Express Entry Year-End Report 2015' (specially check 'Results of Express Entry Invitation Rounds to Apply for Permanent Residence' section) and you'll get more insight.
Please help me to understand this problem. I hope you get your problem resolved now.
All the best...