Hi Jules,
Yes, getting the proper treatment (whatever that will be for your cousin), will help or even correct the low platelet count. It's a matter of getting the disease process quiet. Once it's quiet, the body can repair itself and normalize (as much as possible).
If the doctors are having trouble coming up with a medication formula, your cousin must have some additional issues to go along with Lupus that makes all this more complicated?
I would encourage your aunt and uncle to at least view some of the threads and posts here. The more knowledge they have, the better off your cousin will be. You are doing your family huge benefits by asking questions here. They're very blessed to have you in their lives!
Talk to you soon!
Ginny