Ok.
to me, it sounds like you do have some added problems. He is saying that he does it on purpose. Does he mean he does it on purpose to bother you or does he mean he can't help it...he NEEDS to do it? Is he good at communicating when he speaks?
As for loud stims, I would tell my son to please try to be quieter, but he would listen. He wouldn't stop (maybe couldn't stop), but he would try. You have a different type of child there. I have no idea if he is doing it on purpose or not by your description. Chronic lying is more a Reactive Attachment Disorder (RAD) trait than anything else. I doubt there is only one issue with this child. I would do the neuropsychologist and see. I doubt anyone here can tell you what is going on. We can only maybe guess.
I wish I could be more helpful :<<
