What kind of pain is it? I had sharp chronic lower back pain exclusively on the right side and was referred to a physiotherapist. She came to the conclusion that my lack of activity had weakened my core muscles, and along with the fact I have mild scoliosis, this left me susceptible to backpain. This proved to be correct as my ME has improved quite a bit in the last 8 months or so which means I've been able to do more, and that pain has eased considerably. So it may be a catch 22 situation for you where it's you're inability to be active which is causing it.
However, I get a different type of backpain which I know is actually a symptom of my ME, it's more like an extreme feeling of fatigue which aches and encompasses my whole lower back, and I get it on my bad days when simply standing on the spot. It makes me feel like I need to collapse in a heap. Is this is kind of pain you experience?