I was wondering if an online LyX editor like Google Docs exists or whether there is a project of online editor under development, either within the LyX community or as an independent project?
There's a fully working LyX chat extension, allowing you to LyX-chat with (XMPP) friends: http://wiki.lyx.org/Devel/LyXChat#sDevel.LyXChat_8
There's also a proof-of-concept, badly crashing, extension demonstrating multiple LyX users interactively editing the same document: http://www.lyx.org/trac/ticket/7964
Maybe you will like Authorea - a collaborative platform to read, write, discuss, and publish research. Write in Markdown, LaTeX, HTML, or plain text. Git-like changes management.