Since lazyInit also implies withConnection, I think maybe just a quick search-replace (across all the files) to lazyConnection might be an improvement in clarity for people skimming the code.  I think the key thing is highlighting that the function in question will have a "connection" when it is run.  (The concept of an ActiveSync connection is of course a little weird compared to IMAP since we can't really 'lose' the connection once it's established since it's really a question of knowing what server to hit with XHR's.)