I would definitely keep up the exercise if you can. Just pay attention to your body, if you feel weak, lightheaded, or any pain... stop.
I have seen different responses to doing anything but the lemonade. I'm thinking that the vitamins might not be absorbed right and may move through with the lemonade and flushes. But I don't see much harm.
I recommend seeing how you do with just the lemonade first. If your body is searching for more vitamins, it will let you know. If your workout goes well, then wait till the fast is over.
I'm sure you're aware of the need for water though. This diet calls for it, but the sway in your potassium levels while exercising is important to subside. And as a side note, always hydrate at least 1/2 hour before you exercise. Sipping water is helpful for dry mouth, but if you're thirsty during exercise it's because you're already dehydrated.