The liver is responsible for metabolising usable thyroid hormone (the TSH, T3 and T4 cycle), so the stronger it is the more of an aid it can give to your thyroid.
Since my thyroid was irradiated, Liver Flushing didn't help me much, but it did reduce the amount of synthroid I need to take. I can't take iodine, I get rashes. Iodine is not always good for thyroid people, it can give them goiter.
Julia actually used Iodine to knock her thyroid out when she was hyper, so she coudl focus on the liver without the thyroid going crazy all the time. Once her liver was clean, the hyper condition resolved itself. Wish I'd known this when my own was hyper!