It really depends on your cause of hypothyroidism Arline. There are many causes of hypothyroidism and it can take abit of trial and error, some of the common causes include nutrient deficiencies such as iodine, tyrosine and selenium. Hormonal disorders such as estrogen dominance can effect thyroid function and cause hypothyroidism.
Adrenal insufficiency is another common cause of of hypothyroidism. Treatment will depend on the cause. But yes if a vegan diet is done right it can help with many of the primary causes of hypothyroidism.