You will need to use a proxy and port forwarding in order to have https for your LMS url. Iframe only supports https and NOT http. Then it will work (I have it working). I found this on Reddit which got me started back then:
And this comment: https://reddit.com/r/homeassistant/comments/jkhg1n/_/gamkzwm/?context=1
By the way, since one of the latest HA updates the LMS integration also supports the Media Browser of HA. Just select Media Browser on the sidebar and then an LMS speaker. You can access and play everything in your LMS library through that (including Spotify, Deezer and Tidal if you have Online Music Integration setup in LMS). So if you only want that and don’t want the hassle of iframe cards, you can try that.
But this is getting extremely off-topic, since this thread is about Mopidy/Snapcast and not LMS.