I understand any oil will do the trick. However, the healthiest is the cold-pressed extra virgin olive oil. It seems to be just a matter of health concern.
Mrs Chang from Sensible health does say that as soon as we have our last taking of the mix(OO+Juice) we should lie on our right side. Apparently there is an explanation for this that I just can´t remember. I heard that some people don´t follow this and their flushes seem to work as well.
I, just to be on the safe side, always lay on my right side and so far all my flushes worked out!