I've done a couple of liver flushes.. the lemon (or grapefruit) is to help the olive oil go down and stay down. 2 oz of olive oil mixed well with 4 oz of lemon or grapefruit juice. I have never vomited.
Here is what I have been taught to do:
Juice 2 granny smith (green) apples and drink morning and again at night for 3 days (8 oz. each time). The malic acid helps soften the stones. You can use purchaced apple juice too.
Evening of the 3rd day drink 2 oz of olive oil mixed well with 4 oz of grapefruit juice, the juice from one grapefruit. (Or use 4 oz. lemon juice) I didn't know if I could get this down at first, but had no trouble.
After drinking the oil and juice, lay on your right side with your right knee drawn up to your chest, as far as you can for 20 minutes. (Opens the pathway to the liver)
Before retiring drink a 10 or 12 oz bottle of magnesium citrate
(purchace at drug store in the laxative section for under $1.50)
In the morning you will pass sludge and stones... it works fine and seems easier than some of the suggested methods.