The liver does reportedly play a very important role in “thyroid” health. That’s because the liver converts a huge amount of T4 to T3 (or rT3 if things aren’t going well) and it also creates transport proteins to shuttle free thyroid hormone to cells where it is used. So if the liver is not functioning optimally, “thyroid” health will suffer.
Generally-speaking, the liver needs adequate nutrition/energy to function well. So refeeding tends to help. The liver particularly needs adequate quality protein, and from my research tends to do particularly well with gelatin. Adequate carbohydrates is also important, generally.
As with all things, sleep, rest, and relaxation are important for liver health. Going easy on alcohol is generally advisable. Lowering estrogen is also probably a good idea since that burden falls on the liver to metabolize excess estrogen.
I’m not a fan of using strong herbs indiscriminately. However, there are some pretty safe, gentle herbs that can help the liver. Milk thistle seed is one. It does contain PUFA, but the amounts that are needed are pretty small. It also may contain estrogen. But studies show that the net effect of milk thistle seed actually lowers estrogen in the body due to its positive effects on liver health. Dandelion root is another safe and gentle liver herb. Sometimes, in rare cases, stronger herbs are helpful/necessary. But I wouldn’t turn to those at first.