When I found out about the liver flush, the recipe I used called for 1cup olive oil, the lemon/grapefruit juice, and 1cup coke (coca-cola classic). I have tried the flush with and without the coke and have had better luck with. I also have far less nausea and it is MUCH easier to get down. I know some will object to coke as not being very healthy, and I couldn't agree more. I don't go near the stuff on a regular basis, but I can't see the harm in using it for an occasional flush. Just drink lots of water the next day (A good idea anyway). As far as the other food you mentioned, I don't think it would have the same effect. The protein and carbs would lesson the effect that the fat has. There are probably other reasons as well.
Good luck,
Dave