You have the olive oil, and adding apple cider vinegar provides the citric acid needed for the flush (this is what is in the lemon, or grape fruit, or Coke), and voila!

I guess I will go against popular opinion and say that I think it is entirely possible. Make no mistake about it, it's the oil and fatty foods that cause biel to be released. I think it is why people also experience pain, because of a stone passing through and sometimes getting stuck.

A Liver Flush is designed to withhold fatty foods for awhile, which causes the bile to buildup, and then when you eat fat, especially a good amount of it, the extra pressure forces even more bile out, which propels more stones.