I'm curious what you mean by being reliant on the olive oil and whole lemon drink.
Having a healthful level of good fats in your diet is good for the liver. The liver needs fats to stimulate bile production. Bile cleans the liver as well as triggering metabolic reactions to digest fats. Encouraging the flow of liquids -- lymph, blood, bile -- cleans and nourishes our bodies. Think of the liver cleanse as excercize for your liver:)
The liver cleanse works best when the liver is producing generous quantities of bile. That is likely the case with you, since you've been drinking olive oil daily.
Disruption of the normal pattern is the key to the cleanse. The body is used to eating fats, so it doesn't stop producing bile when you don't eat fat in the pre-cleanse. When you drink the oil mixture, the large intake of oil stimulates even more bile production.
I strongly encourage you to do a low-fat pre-cleanse, without drinking the oil mixture. If you can't do that, I question whether the flush is for you.