You don't have to put LMIA number if you don't have one...
In my case, I thought because I am working already and will continue to work, it counted as a Job Offer. It then goes on to ask you questions about this job...LMIA number, work permit details (Open or closed) etc. I was truthful in each answer and did not receive points for 'arranged employment' in my ITA, which would be the 'job offer.' Therefore, if the case is anything like mine, I agree write a LOE with extensive reasons as to why you got it wrong or accidentally 'misrepresented' yourself.
Scary thought that our future is in the hands of an Immigration officer whom doesn't know much about us!