My current nanny is in the LCP. But, before we hired her and helped her get into the LCP, she was just a regular TFW, working as a nanny for someone. She had her own apartment. She was just classified as a TFW, and her work permit then said something like "nanny/babysitter; not eligible for PR; not LCP".
She would have worked for this man from about 2010 to 2012. I am not sure CIC is still granting regular TFW LMO's and permits for nannies. Someone at CIC told me they wanted all TFW's who were working as nannies being processed under the single banner of the LCP. So I thought maybe they were phasing out this practice. Not sure though.