I am sorry to hear that you have lower back pin when you don't eat for an extended period of time. I recommend that you make an appointment with your primary care physician
to discuss your problem, and to have a thorough physical exam. I am not trying to imply anything by this, but sometimes patients that have eating disorders have malnutrition bad enough to cause atrophy/breakdown of muscle, and even bone to the point that there can be destructive changes to the spine. This doesn't fit perfectly in your case since the back pain seems to be transient and related to not eating. My best guess is that you may be having stomach/intestinal pains that are being referred as pain in your lower back.
also you are correct in saying that kidney problems can give back pain. If I assume that you are not drinking when you don't have time to eat, then you may be dehydrated and could potentially have kidney irritation that is referred as back pain. I hope that this at least gives you a little insight into some possibilities as to what might be going on. Try starting out with an appointment with your primary care physician. Best of luck.