I don't have any experience with thyroid, but I do know that a lot of people beginning low carb have a couple of weeks of 'blah' energy at first. It goes away as the body adjusts.

Rather than trying to fight the lethargy head-on, maybe you should reintroduce exercise slowly? Start out with walking, then maybe slowly build up to your previous program? I'm no fitness guru, but I have lots of experience with setting huge, unattainable goals for myself, and I'm slowly learning I have to be more realistic about my abilities.

Rachel