I would like to know if it is possible to have playback info from lms plug-in (logitech media server) in the volumio app or http: //volumio.local?
If “playback info” is not already provided by the plugin, then you will need to contact the plugin author for more information.
I think it should be possible to create a listener, you can raise an issue on github. However, you can debate whether the player or server should propagate to the UI 
If the player should be leading, here’s that repo
PS: to manage expectations, I have a lot of other work in other plugins (e.g. experimenting with Docker for SnapCast), so don’t expect a patch soon.