My goodness...the olive oil and citrus juice never enters or goes through the liver!
The oil and citrus cause the liver and gallbladder to contract - I think we are all agreed on this point - releasing stagnant bile, toxins, parasites, cysts, etc. into the intestines. The purge then may coagulate with the olive oil in the intestines, forming what we call "stones" in the process. If these stones are indeed formed outside of the liver, the stone-content is still stagnant bile, toxins, parasites, cysts, etc., along with, perhaps, the oil.
Regardless, the exact procedure is not entirely relevant. What is relevant is that the liver and gallbladder purge their contents (or some of their contents) and this release is later excreted via the anus. The purification of the liver, gallbladder and colon, along with the resulting restoration of organ function is what heals the body via their return to natural efficacy.