Frankly speaking, I have never seen one web application that can smoothly transition between online and offline states and works great in both states. If I were offline, I’d rather read a book.

LiveView itself will probably never support client-only directly.
However, there are two developments in this space which might open up interesting possibilities in the future:

• elixir_script which compiles (currently a subset of) Elixir code to JavaScript. With this, someone could make a library that accepts the same syntax as LiveView-behaviour modules but which would compile down to JavaScript and thus be fully client-side.
• lumen, an alternative BEAM (the Elixir/Erlang VM) implementation which could conceivably compile through WebAssembly to run fully in the browser.

It’s not strictly server side. You can’t just do offline LiveView web apps. There is this new project GitHub - elixir-desktop/desktop: Building Local-First apps for Windows, MacOS, Linux, iOS and Android using Phoenix LiveView & Elixir! · GitHub that allows you to use LiveView to create mobile and desktop apps. But for strictly web browser based UI you need to have WebSocket connection connected to server for everything to work.