I'm so very sorry about your sister. Unless the hospital is lyme literate, I wouldn't go there. I don't think your sister is dying. I'm not a doctor but have been around lyme disease for many, many years and it sounds to me (just my opinion) that your sister may be suffering from an overload of toxins.
I just started a new post about detoxing. See if your sister can tolerate a detox bath using lukewarm water. Those toxins need to come out.
You can e-mail me if you like.
Good luck to you and your family,