If it really wasn't sanitized properly there is definitely some fault with the MUA, but I highly doubt she applied it to this woman without her permission, so the ultimate responsibility has to lie with the customer.
I see it as a personal responsibility issue. If I know someone hasn't sanitized a product, and I still allow them to apply it to me, I am choosing to take the risk of catching something, and by taking that risk it's then my fault if I do.
Even setting aside the issue of proving the herpes cam from the lipstick, it just doesn't seem like a suit that holds any weight:
"I knew she hadn't sanitized it, but I let her apply it to me.
I caught herpes and it's her fault because she didn't sanitize it."
"Well you knew she hadn't sanitized it, so why did you let her apply it?"