Are you still suffering from the signs of chronic Lyme Disease or post-treatment Lyme Disease syndrome after treatment with antibiotics? You are not alone — and like others in the same boat, you may wish to turn to alternative or novel therapies in the quest to liberate yourself from the debilitating symptoms that are robbing you of the quality of life you deserve.
What Are Stem Cell Transplants?
Stem cells are, as the body's "key" or "master" cells, pretty exciting. Some have the potential to turn into a limited number of different cells, while others can literally become any cell at all.  While the term "stem cell transplant" won't be familiar to everyone, the concept is — you'll certainly have heard of bone marrow transplants, which are a kind of stem cell transplant. Medical advances mean that stem cells can also be taken directly from the bloodstream now, as well as from cord blood or extracted from a placenta (embryonic stem cells).
The transplanted cells may attack the recipient's cells after perceiving them as foreign in graft versus host disease, and the chemotherapy required before the transplant causes its own side effects as well as placing the body at risk of opportunistic infections, anemia, and bleeding.  It goes without saying, really, that stem cell transplants of any kind should only be performed on the right candidates and that careful risk vs benefit analyses need to be carried out before a stem cell transplant takes place.
Is There Any Evidence That Stem Cell Transplants Could Benefit People With Post-Treatment Lyme Disease Syndrome?
Yes, there is some. One small study investigated the merit of human embryonic stem cell (hESC) therapy in two patients with both Lyme Disease and Multiple Sclerosis. Administered in various ways, including intravenously, intramuscularly and in the form of eye drops, both patients "showed remarkable improvement in their functional skills, overall stamina, cognitive abilities, and muscle strength". The study authors concluded that further clinical trials would be warranted to determine whether embryonic stem cell therapy could be applied more widely in the future. 
This treatment may just hold promise, but we still currently have a situation in which we are "without recognized therapeutic effects on Borrelia burgdorgeri to stem cell transplantation" . Meanwhile, stem cell treatment is already offered to patients with purported "chronic Lyme Disease". I searched what kind of protocols are being marketed to people in this group, and those I came across combined stem cell therapy with other (unproven) alternative therapies for Lyme Disease, such as enzymes, ozone therapy, and a targeted diet.
"Stem cell therapy" doesn't just sound exciting and futuristic, it also has a decidedly scientific ring to it that may induce trust even in people usually skeptical toward non-mainstream medicine. The US Food and Drug Administration (FDA) warns, however, that that trust isn't always deserved:
"The Food and Drug Administration is concerned that some patients seeking cures and remedies are vulnerable to stem cell treatments that are illegal and potentially harmful. And the FDA is increasing its oversight and enforcement to protect people from dishonest and unscrupulous stem cell clinics, while continuing to encourage innovation so that the medical industry can properly harness the potential of stem cell products." 
It goes on to advise patients interested in stem cell treatments to make sure that the particular treatment they are considering is either FDA-approved for the purpose they are considering using it for, or currently being investigated as part of a clinical trial. Because some clinics will advertise clinical trials, the FDA notes, without going through the proper procedure, it is best to check with the FDA directly — if, of course, you live in the US.
In a separate statement, the FDA goes into more detail, warning that "these cells are [often] being used in practice on the basis of minimal clinical evidence of safety or efficacy, sometimes with the claim that they constitute revolutionary treatments for various conditions".  Such is currently the case with chronic Lyme Disease.
Using stem cell treatments in the treatment of a wide variety of diseases and conditions without well-established evidence that these treatments are both safe and effective for the purpose in question puts patients at risk. As a patient for whom this treatment may be a last-ditch attempt to get better, pursuing a novel therapy that holds some promise may make sense. When stem cell therapy is not available locally, many decide to travel abroad — a practice known as stem cell tourism . We'd advise you to discuss the merits of this with your treating physician in great detail, and also to familiarize yourself with the standards of care and regulations in the country you are considering traveling to, and ultimately to err on the side of caution.