I am on the pill, and my first month of LCing, my period came a week early. I called my OB/GYN and talked to a nurse about it. I explained my WOE, and the situation. She said it probably was the diet, and I should continue to take my pills every day on schedule. I did, and everything has been on time since. I have noticed that my period has been lighter since I have been LCing, so that makes it a little bit more comfortable to bear. Good luck!
Julie