For Live Stream Closed Captioning, ShowTix4U first recommends that you first consider adding an American Sign Language (ASL) Interpreter to your Live Stream via picture in picture. Most broadcasting/streaming applications allow for 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.