Is there any lyx online editor

You can use LyX online at rollaps. There have been efforts made in the past to allow collaborative (e.g. simultaneous) editing in LyX, but these have not made it far. See e.g. this Google summer of code 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