coopergrrl- I don't know much about LAWL, but I unfortunately know a lot about fibro and thyroid issues. Does the LAWL food contain soy for protein? If it does, it's messing up the uptake of your thyroid meds which could be causing the fibro flare. Or you could just be having a reaction to some ingredient in the LAWL foods that is causing the flare.
I avoid any soy based protein like the plague. I can pretty much count on having a fibro flare if I eat it. I'm not on thyroid meds now, but the soy-thyroid link is 100% proven.
Check the ingredients labels on whatever you are eating
Good luck figuring it out!
Mel