I started the diet the 2nd of this month, and I too thought I could continue weightlifting and exercising in general. After starting this diet, I have literally lifted/exercised only a couple times and have lost about 10 lbs. You just will not have the energy to exercise after starting. You will lose weight due to the lower calories in the vegetables you eat (even if you eat alot as i do) as well as cutting out the carbs, if weightloss is a goal. I incorporated eggs pretty heavily in my meals to start, and have added more chicken and fish now to curb weightloss.
Also, Able and Raster both suggest to take some time with only very light exercise if any to give your body time to heal as it will already be overloaded with the diet. The minds behind this forum (A & R) suggest sauna or steamroom for a good sweat as well as releasing toxins.
Number 1 rule in my opinion for diet, exercise, or anything else for that matter is listen to your body. It will tell you what you can and cant handle. Give it time to adjust.