I would always err on the side of caution - remember that you are actually injecting Botulism into your skin. With a lowered immune system, I would be very careful even though it's not an live bacteria.
I found some info that explains how it works here:
www.bellspalsy.ws/botox.htm"It is a genetically engineered protein that weakens or inactivates muscles. After injection Botox enters the nerve ending of a muscle, binds to pre-synaptic receptors and blocks transmittal of nerve impulses at that point. The muscle will not contract because the signal from the nerve has been stopped."
Since Lyme attacks nerves and blocks the signal or interrupts the signal that comes from the brain to that muscle, it doesn't seem like a good thing to do - at least while a person is battling tick-borne infections - but that's just my opinion.