If you don't want to pay owncast is a good option, if on phone you can spin up node-media-server and use BroadcastMe and fire the link up a kind1 or a kind 30311(streaming event) note. The lag will depend on the connection in any case.
You can use the built in service that zap.stream offers. OBS or Owncast.
Nogood radio + zap.stream on podbean, because why not:
https://video.nostr.build/ddcb9c398bb593bb328fc47d181c233b50d5babac341ecd32cd9da3aa81b5562.mp4
How it looks like on podverse:
https://video.nostr.build/649a7a9ab3b25620debd34c4613587281d7bb223ea6c291c309f0c4abda89407.mp4
How it looks like on podcast republic:
-media url or direct share
How it looks on fountain:
-picks up the whole feed not just the notes with media, which is annoying
-very slow picking up from rss, usually helps if adds the episode to library
-no proper info linking
https://video.nostr.build/5e742c77df01c1b2a4e01b67f7999bee3353d79cc398738bd06528b2fbd45b7a.mp4
Sharing from antennapod to oxchat or else: 
How it looks on antennapod:
- it pics up the whole feed which is annoying
-does not play m3u8 but can be opened through 🌐 and the nostr app
-does not play video directly but 🌐 in browser
https://video.nostr.build/b82884b6ae1cbc518c51969410fc80dc7768bb8f2324970ff899cf9885ca42f3.mp4
https://video.nostr.build/f0fd34d5c9f9309fffa9213869b3bba6ee0b36a39286fcc4f558eff08167db6f.mp4
Virgin Classic rock http://icy.unitedradio.it/VirginRockClassics.mp3