The download page has the whole codebase in its entirety, GPL licensed: http://luminotes.com/download

The link to this page is at the bottom of the front page. It used to be more prominent, but I found people got confused about whether they had to download the software in order to just make a wiki.

You can browse the Mercurial repository online as well.

And as for your question about keeping the software in the "cloud".. The software actually does have some sharing/collaboration features. (Whether they're useful for your specific needs is another matter.)

I'd like to make a desktop version of Luminotes at some point, but I have no concrete plans for it now.