I'm sticking with Atkins while I do my challenge. Read the sticky at the top of the page that answeres many of the questions about combining BFL with low carb.

For your after workout meal have no fat and high protien/carb. This is where egg whites would be good (I buy the little cartins just to make it easier). The rest of the day eat LC including your whole eggs, higher fat things, and no potatos ect. You can also just save the yolks to make mayo, cheesecakes and so on

Or you can do the BFL menus and ratios. It may be a good idea to choose one or the other though. If you have high carb and high fat, that is very bad. Having a moderate amount of carbs (much more then Atkins induction) with a moderate amount of fat shouldn't be a problem though.