Short answer: While it does help to do a Bowel Cleanse first, it's not required.
Longer answer: However, it IS recommended that the released 'stones' be able to pass through your system as quickly as possible. With that in mind, you may want to use a saltwater flush the morning of the day you plan to drink the oil-juice mix, or an enema or home colonic (colema) sometime that afternoon and another the next day. Even better, instead of the enemas and if you can afford it, might be to schedule a colonic for the next day.
Personally, I drink the saltwater flush 1st thing in the morning, before ANYTHING else, followed an hour or so later by a banana or apple (or juice my own fruit drink). (Then for lunch I have a mixed green veggie salad. NO FAT.) I drink a LOT of water on flush day, more than usual, and I drink all 4 of the Epsom Salt drinks. The Epsom Salt drinks are VERY dehydrating, but they're a pretty good quick laxative as well helping all those 'stones' get of FAST.
As long as you have some way of getting those nasty little 'stones' and their side baggage of toxins out FAST, it should be ok to go ahead with a liver flush.