I wouldn't lift twice a day, either on cycle or off. Even though I do believe in training more frequently than is the conventional wisdom, there is always a point of finishing returns. I'm pretty sure that for anyone, lifting twice a day is at that point.
If someone wanted to add in a second session of cardio each day, I don't see how that could possibly be a bad thing. Cardio actually helps with recovery from weight training, which is another reason to do cardio after you lift. Adding in another session each day is only going to burn some more calories.