Lithium causing hypothyroidism and Hashimoto's?

I've been on lithium for almost 2 years. I'm down to 600mg a day now but before I was taking 1500mg daily. it was so much it was causing me hypothyroidism, so they put me on levothyroxine. they said my bloodwork showed that the hypothyroidism was getting worse as my lithium level increased. this was all while I was in residential, and managed by the doctors there (who I don't trust for other reasons I won't get into.) when I was discharged from there i got a whole new set of doctors. they say I have hashimoto's. now I'm on less lithium, and they say the hashimoto's isn't doing anything and they only know about it from the blood tests. is it possible for all of these things to be true?