It is real-time editing! We leverage web-sockets to sync across multiple logged-in sessions. But as of today it does not support multiple users collaborating on the same document.
Right now we don't have support for a local storage mechanism or self-hosting. We are extremely keen on privacy and are very open to working towards either of those two options.
Lowercase really shines when you want to take notes free-form and then be able to share those notes out into the world. You can easily make a note public & even cooler than that you can turn a lowercase note into a presentation with just a few clicks.
There was an app that did something related to this called facewash (renamed to simplewash) https://www.facebook.com/simplewash/, but it seems to since have been shut down. May be worth it to shoot them a message