Don’t know about your client, but on #damus, images are uploaded to an ordinary HTTP server and linked into the note, not inlined.
Advantage: simple
Disadvantage: very centralized and not very censorship resistant
Discussion
That was my point. A livestream would work the same way, and it's just a matter of the client rendering it inline or not.
By the way, this is usually done via oEmbed around the rest of the Web: https://oembed.com