Hi lymiemom, welcome to the board! I am sorry you are having this symptom, I know it is very upsetting.
Both Lyme and thyroid disorders can cause hair loss. It is important to get the Free T3, Free T3 (besides the T3 and T4) and thyroid antibodies tested. Have you had these levels tested? Many doctors do not test these levels and treat only by the TSH result. If antibodies are present, it can indicate Hashimoto's Thyroiditis which is an auto-immune thyroid disorder. Some people who have Lyme have this. Lyme and hypothyroidism have many similar symptoms.
Do you have a copy of your latest thyroid results? Which thyroid medicine are you taking? Some thyroid meds such as Synthroid is a T4 only med and meds like are Armour are a T3 and T4 med. Some people do well on one type, some on another. Depending on what your Free T levels are, you may need an adjustment in your thyroid medication. It took me a long time to find a doctor who could properly treat my thyroid and who worked with my symptoms, but it can make a big difference.
Have you ever had your cortisol and other hormone levels tested? Lyme can affect all of these levels. It is my understanding that saliva testing is more reliable than blood testing. If you want information on saliva testing, let tme know.