Hi, I love lavender oil, but have stopped using it because of advice from my nutritionist. Lavender oil, he said, can especially have a detrimental effect on your thyroid, which might be why you have hair issues in the first place. If you feel you want to continue with the lavender oil, you might consider mixing it with some coconut oil to help oppose the estrogens and unsaturated fats in the lavender oil. Coconut oil alone is said to do a lot to help repair hair and there is feedback on this site regarding it as a remedy. Coconut oil also has so many wonderful attributes and helps the whole body.
Essential oils are polyphenols, which are estrogens, and many of us are estrogen-dominant anyway. Likely as a result of my over use of essential oils in the past I have had the experience of remedies that work great for other people actually working backwards on me! It has made my case a real challenge for my nutritionist. And the only people he's worked with who react the same way I do are people who have used a lot of essential oils. There is a reason why nature puts only a tiny amount of essential oil in one plant or flower, because essential oils are very powerful substances and we really no so little about them.
Essential oils are also unsaturated fats. Saturated fats are the best for you, things like coconut oil, butter, palm oil and olive oil.
And one of the side effects of a poorly functioning thyroid, as well as estrogen dominance, is thinning of the hair.
Best of luck as you research your health.