You can use OSYouTube plugin to display YouTube Live videos.
- Visit youtube.com
- On the left sidebar, click "Live":
- This will bring you to the "Live" page, listing the videos currently streaming live. Click on the live video you wish to embed in your Joomla site:
- You will see the screen with the video streaming live. Click "Share":
- This will open the "Share" box. Click "Copy" to copy the URL of the video to use in your Joomla content:
- Open the required Joomla content item for editing. Paste the copied link as you see fit:
- Click "Save" or "Save & Close".
- Test this content item at the frontend of your Joomla site. You should see that once you clicked on it, the video is live streaming: