I just checked now and there is a very slight lag, maybe on the order of 100-200ms. It's pretty subtle though and I definitely did not notice it before you mentioned it. I can imagine that it would be maddeningly slow if it were something like a rhythm game or a musical instrument app though.

Yeah that's what I was referring to. At one point, I thought I was going to wirelessly connect my electric keyboard at home to my stereo through a bluetooth transmitter. I soon found out that there's a delay associated with audio transmission through bluetooth. I don't think anyone's really solved this problem for these kinds of applications because most people use bluetooth audio for passive tasks like listening to music.