Consult an immigration lawyer. You don't necessarily need one to complete the applications and submit the paperwork, but an initial consult will let you know what your options are, the risks, and what timelines you're looking at.
I can give you some general information, but I've been out of the immigration world for the past 6 months -- of course, many TFW programs have been completely overhauled during that time. For instance, it's not even called an LMO anymore (it's now a LMIA). So a huge caveat on what you're about to read:
First, you can't appeal a decision regarding a rejected LMO or work permit -- you simply reapply. In the case of food services workers, I think the moratorium has since been lifted, but I'm not sure if there are any new conditions. As posted above, the LMO itself is only the vehicle to get a new work permit, which is what she needs to stay in the country (assuming she wants to work; another option is to apply to extend her stay as a visitor but that would be a last resort option -- she legally can't work as a visitor).
I also note the difference between temporary residence (via a work permit, student, or as a visitor) versus permanent residence. She'll need to get the former figured out first (assuming she wants to stay in Canada); the latter will have to be dealt with afterwards; the issue of Canadian citizenship doesn't enter the conversation until after she has become a permanent resident (aka "landed immigrant").
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