If you are having blood work done, ask them to check your thyroid levels.
Hypothyroidism can cause coarse/thinning hair.
At the very worst, you can cross it off your list if the results are negative.
For what it is worth, here is a link I found when searching for hypothyroidism and lyme :
I woke up one morning BALD on my left side ( worst affected side of my body ) ...actually this was quite a relief , in a strange sort of way. People had been telling me there was nothing the matter with me for so long - and as soon as I had this ( cosmetic ) problem all the doctors suddenly sat up and listened. I polished my bald spot whilst re-telling them all what I had been telling them for a year. Only NOW they listened. They believed me . The hair grew back . Almost at the same rate as my self confidence.
NB Thyroid / Adrenal / Pituitary tests were normal throughout !