I'm yet to start CD, but I did LL for 16 weeks. I exercised from day one without problems, but I started off relatively slow. I was used to doing 30 mins on a Nordic Track ski machine, but on my first week of LL, I did 20 mins/day and was tired-ish. Within a week, I upped it to 25, then to 30, then to 45 mins. I couldn't go much higher than that, as I'd feel really knackered and a bit sick if I tried to push it much past 45 mins.
I found it really helped me in my first week to exercise as it stripped my glycogen stores and put me into ketosis that much faster. If you do exercise, though, drink lots of water. I found that I'd drink about a litre of water whilst exercising and a litre afterwards, even in the shower after my workout. I don't think the exercise really helped me lose weight faster, but it does help you feel and look better in your clothes. I've had a VCLD break in between LL and CD and I haven't gained a pound in the past month from my final LL weight. Not lost, either, but not ballooned like I was worried I might. :happy036:
I'll let you know when I start CD a week from now if I notice any significant difference between LL and CD exercise.