For Live Stream Closed Captioning, CUR8 first recommends adding an American Sign Language (ASL) Interpreter to your Live Stream via picture-in-picture. Most broadcasting/streaming applications allow for the easy addition of picture-in-picture.
You could also consider using PubNub or WebCaptioner with a broadcasting/streaming application. This is an easy way of "burning in" closed captioning to your live stream. However, this is not as accurate and also not available for music vocals.