Can I/do I have to workout on keto?

Yes you CAN, and yes you SHOULD.  When we talk about a healthy lifestyle, daily movement needs to be part of it.  Remember, the goal is fat loss, not muscle loss.  Without any exercise, it is surely possible to lose weight with a ketogenic way of eating, however, some of that loss could be muscle density.  Incorporating exercise into any nutrition plan will yield better, faster results.  When the body is fat-fueled, you will notice an increase in energy and endurance, allowing you to power through your workouts and hold onto strong, lean muscle.