So having been around for several discussions on Lumen (I’ve worked on the site) I don’t think Erlang distribution is intended for client-server communication there.
For one thing Erlang distribution lets nodes run code on each other. Remote Code Execution as a service 
Lumen could, when ready, certainly let you write Elixir for your frontend or potentially re-use your server side logic on your client. I think that could be an addition to LiveView. I doubt it would be inside of LiveView.
There are serious challenges to overocme anytime you want to do good offline and good online. If/when Lumen ships it could be part of making that possible by writing only Elixir.
For now I’d look at what can be done using LiveView JS commands. I haven’t dug into it though.
