Infectious disease is not my area of specialty, but what I do know about Lyme disease and stem cell technology leads me to believe that efficacy of stem cell therapy is inconclusive. There are many places (especially outside the USA) now offering it as adjunctive treatment to the antibiotics, but there is also surprisingly little outcomes data available. They charge a lot of money for these treatments (tens of thousands of dollars), but I am yet to see results that back up some researchers' claims that it is a viable treatment for Lyme disease. They can't say for sure that the symptoms of the disease went into remission because of the stem cells treatment. For many people with chronic Lyme disease, those symptoms come and go---typically with no particular pattern or regularity. There is some old, anecdotal stuff out there about stem cells that allegedly helped people with Lyme disease, but nothing that I would rely on for making sound clinical decisions, in particular about expensive stem cells modalities. For how much it costs, we should be seeing a lot more conclusive evidence of successful treatment outcomes in this area. I would love to be able to tell you that it works, but the data to support that (one way or the other) just isn't there. STILL, if you can afford it it's certainly worth giving it a try---especially if your little girl is a chronic who's now having cognitive anomalies.
I put special emphasis on the last sentence in the previous paragraph because medicine is strangely more art than science; sometimes some therapies work for some people but not for others, and we don't really understand why. Some clinicians will make up a bullshit story to impress their clients, but when I don't know I come straight out and say that I don't know. And this particular treatment is definitely one of those things that no one can say will work with any degree of certainty or even at all.