There was a very popular diet going around a few years ago. The "Mayo Clinic Diet" (which happens to be in MN--probably why I came across it) that was supposedly for heart patients who had to lose a lot of weight before surgery. I am sure that there were several versions of this diet, but the one I saw, and tried, was basically Atkins, with unsweetened grapefruit juice before each meal. It did work.
I guess it would be a matter of deciding which diet you want to follow. I think it would kick you out of ketosis, but you should (and I stress should, not will) lose weight all the same. It's just a different method.
This thread caught my eye because I am TTC and don't want to be in ketosis, but still want to lose weight. As it happens I bought grapefruit juice last night. It has 25 carbs per cup.
If Atkins is working for you, I would stick with it. If not, you may want to try it. As I said, I did lose weight on this in the past, however, I lost weight faster on Atkins.
Then again, it may all be a hoax, who knows!! Just the fact that you are cutting out the "junk" carbs could cause the weight loss, not the juice.