There are some great comments and advice in this thread imo.

Based on my own experience I wouldn't exercise much except perhaps something low intensity like walking during induction. When I did low carb the first time in 2005 I did an induction period during which time I attempted to continuing doing high intensity weightlifting workouts without much success. I had the usually loss of energy and headaches reported by many people during the ten days or so I did the induction.

This time around which started two years ago this month I didn't do an induction at all but just tried to get carb levels down and fat levels up while trying to eat mostly clean protein (lots of fish and chicken). I had zero problems doing high intensity workouts during my transition from a SAD to a low carb diet. Now that I'm thoroughly acclimated to the low carbing I feel like I have more energy and endurance than ever before. I frequently play singles tennis (USTA 4.0 fwiw) and have not had an instance where someone wore me down. At 50+ I'm still the guy running the wind out of guys 20 or 30 years my junior.

I still try to walk about 45 minutes every day because my dogs and I love it so but I think it has other benefits besides the psychological ones.

Also FWIW, I've come to the conclusion based on my two experiences with low carbing that induction isn't necessary. It may (and I think the jury is still out) speed up the process but I think a lot of the initial weight lost in induction is just water and glycogen anyway but imo you can get to a weight loss goal and better well-being without it.