I asked the same thing in a different thread. Here are the replies I got (not sure if My Happy do live-stream translation coverage):

Quote Originally Posted by jameseoakes View Post
Normally one of the community team does a running unofficial translation (here's an example from one of the last ones http://forum.square-enix.com/ffxiv/t...-Update-Thread) and several people do some web-streams and the like where they try to do live translations.
Quote Originally Posted by Theodric View Post
There's a FF14 Reddit Discord group, supposedly - and typically there's live translations in one of the channels within it whenever there's a Live Letter that needs to be translated. I'm afraid I don't have the link myself, though.