I found this from here:
So I guess eventually they do get killed off.http://lymemdbasics.blogspot.com/2013/02/what-is-cyst-buster-and-do-i-need-one.html#!/2013/02/what-is-cyst-buster-and-do-i-need-one.html
What is a cyst buster and do I need one Lyme bacteria are pleomorphic. This means the organism can take on various physical form. Free spirochetes are long, thing, twisting bacteria. Under threat Lyme spirochetes can form blebs which become spherical objects call cysts. The cyst have different biological properties. Antibiotics which previously worked on the spirochete form are no longer effective. Some people refer to drugs which have the ability to kill the cyst forms of Lyme "cyst busters."
It is known that some antibiotics, such as doxycline, promote conversion of active spirochete forms into dormant cyst forms.This does not mean you need to use an anti-cyst drug. First, the cysts are inert and may not be causing symptomatic disease - second, when cyst do convert back to spirochetes, as they are apt to do, doxycyline is in waiting to take them out. Over time, the total Lyme bacterial load, spirochetes and cysts is reduced. Some drugs thought to be only spirochete drugs also show some anti-cyst activity, like amoxicillin.
The prototypic anti-cyst antibiotic is Flagyl, which is also anti-parasitic. A newer drug, Tindamax, is more effective in my experience.
I have found that adding a drug like Tindamax to drugs like doxycycline or Zithromax is a way to decrease overall Lyme numbers more quickly. Some doctors like to give these cyst-busters in a pulse pattern.
The answer is, you do not necessarily need to use a "cyst buster."