Well, I am not qualified to answer your question. But from my own experience, I formed Gallstones when I started to lower my cholesterol. In fact, I was so inpatient and did a huge lifestyle and diet change that dropped my cholesterol VERY rapidly from upnormal to normal in a period of one month. I didn't know that I was harming my body by doing so. So for sure Gallstones can be formed when the body tries to get rid of cholesterol. I have read that rapid weight loss has a great impact on gall stones. My doc confirmed what I read too. Again, this might be true for some people only, I don't know.
I read here that some people were successful lowering cholesterol by flushing. You can look for those posts. Good luck!