We just finished assisting someone who was a regular TFW living and working in Canada to get into the Live-In Caregiver Program. It is possible to switch into the LCP from inside Canada, but our experience was that it was quite complicated.
Here is a link that tells you WHO can apply for the LCP and what you need to qualify:
http://www.cic.gc.ca/english/work/caregiver/apply-who.asp
Major requirements include proficiency in English or French. You must also have a high school diploma (or equivalent from your home country). You have to have at least (i) six months' relevant training, such as a nursing degree or a teaching degree or other child care diploma; OR (ii) one years' experience with caregiving.
There are other requirements as well, just read the information in the link.
We did manage to have our future nanny apply and get into the program without leaving the country. But she did have to apply to a Canadian embassy OUTSIDE of Canada. This can lead to complications, for example, if they call you and require an interview (because then you might have to travel to that place outside of Canada for an interview). Most TFW inside Canada who want to apply to the LCP seem to apply to Buffalo or Seattle, or I suppose to the Canadian embassy in their home country. We applied to Buffalo. They did not require an interview, thank goodness!
It took us 3.5 months to get the LMO. Then it took 2 months once she submitted her application to Buffalo. Once Buffalo approved her application, she then had to travel to a border crossing and "flagpole" in order to get her work permit. All together, it took us about 7 months total.
Anyway, it is possible, but it can be tricky, and you must apply to an embassy OUTSIDE of Canada.
Good luck to you!