Only certain accounts are able to have their live events embedded on other websites. Follow the instructions found here to learn how to embed a live broadcast.
If the iFrame code populates a place holder that links to the event page on livestream.com rather than embedding the live content directly on your website, it's likely due to the account hosting that event not having a Premium or Enterprise plan with Livestream; not all account types include live embedding.
You can also embed a Video On Demand (VOD) clip from any type of account. Click the Posts icon on the event and click any of the posts listed.
When the clip loads on the page, keep your mouse hovered over the player to reveal a few icons in the upper right corner. Click the Share icon.
You can either share the URL which will direct viewers to livestream.com, or click the Embed tab to get the embed code for the VOD.
Copy and paste the iFrame code onto your website, blog, etc. to share it with your followers. Your web domain must support iFrame codes in order for the embed to work.