PS -- I just did a short walk on line through current commentaries on BCA, one of the labs mentioned here, and there were (as with many things in life) complaints about the facility. Since I had posted above that my recollection of years gone by regarding BCA was positive, I thought it useful and fair to note that there are other (apparently more recent) views.
I have never been to the facility or been treated by their staff, and to the best of my recollection, I have not met or personally know anyone affiliated with BCA in any capacity, whether staff or patients.
Welcome to MedHelp Lyme --
I don't have a direct answer for your questions, but someone else here may. BCA is the only lab I recognize in your post above, and my recollection from a few years ago is that they were well respected.
I would ask any MD or lab that you are considering for testing your mother whether the lab is able to confirm or to rule out infections from where your mother lives or has lived previously, and possibly even before she became noticeably ill. This is on the theory that some of us have carried some version of Lyme without knowing we are ill ... and so it's not always clear which strains the patient may have been exposed to and still carrying now. Someone else here may have a better response than mine to your question.
All good wishes to you and your mother, and please let us know what you decide to do and how things go.